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Journal articles on the topic 'Chern-Simons forms'

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Published: 10 December 2022

Last updated: 29 January 2023

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1

Hamdan, Suhaivi, Defrianto Defrianto, Erwin Erwin, and Saktioto Saktioto. "Topological Gravity of Chern-Simons-Antoniadis-Savvidy in 2+1 Dimensions." Journal of Aceh Physics Society 9, no. 3 (September 1, 2020): 65–71. http://dx.doi.org/10.24815/jacps.v9i3.16635.

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Pada artikel ini akan ditunjukan analisa dari perluasan gauge invariant exact dan metric independent untuk menkontruksi lower-rank field-strength tensor. Hasil ini akan digunakan untuk mengkontruski ulang Chern-Simons-Antoniadis-Savvidy formasi (2n+1) pada dimensi genap dengan menggunakan pendekatan diferensial geometri. Selanjutnya akan dianalisa bentuk topological gravitasi 2-dimensi yang merupakan perluasan dari teorema Chern-Weil yang telah dikembangkan oleh Izurieta-Munoz-Salgado. Hasil dari penelitian ini memperlihatkan bahwa aksi Lagrangian yang sama seperti pada topological gravitasi Chern-Simons forms pada dimensi (2n+1) invariant terhadap Poincare group SO(D−1,1) SO(D−1,2). This article determine and analyess of the extended gauge invariant exact and metric independent to construct the lower-rank field-strength tensor. These results used to construct Chern-Simons-Antoniadis-Savvidy (2n+1)-forms even dimensions using a differential geometry approach. This result analyzed 2-dimensional topological gravity forms that extended Chern-Weil theorem which has been developed by Izurieta-Munoz-Salgado. These results show similary topological gravity Lagrangian action of Chern-Simons forms (2n+1)-dimension invariant under Poincare group SO(D−1,1) SO(D−1,2).Keywords: Gauge theory, field-strength tensor, Chern-Weill theorem, Chern-Simons-Antoniadis-Savvidy forms, topological gravity

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2

Konitopoulos, Spyros, and George Savvidy. "Extension of Chern-Simons forms." Journal of Mathematical Physics 55, no. 6 (June 2014): 062304. http://dx.doi.org/10.1063/1.4882086.

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3

Balcerzak, Bogdan. "Chern–Simons forms for ℝ-linear connections on Lie algebroids." International Journal of Mathematics 29, no. 13 (December 2018): 1850094. http://dx.doi.org/10.1142/s0129167x18500945.

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This paper considers the Chern–Simons forms for [Formula: see text]-linear connections on Lie algebroids. A generalized Chern–Simons formula for such [Formula: see text]-linear connections is obtained. We apply it to define the Chern character and secondary characteristic classes for [Formula: see text]-linear connections of Lie algebroids.

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4

Hamdan, Suhaivi, Erwin Erwin, and Saktioto Saktioto. "Chern-Simons-Antoniadis-Savvidy Forms and Non-Abelian Anomaly." Journal of Aceh Physics Society 8, no. 1 (January 21, 2019): 11–15. http://dx.doi.org/10.24815/jacps.v8i1.12796.

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Kuat medan tensor yang ditransformasikan secara homogen terhadap perluasan transformasi gauge memenuhi bentuk sifat invarian gauge. Analisa invarian gauge dalam bantuk integeralnya memperlihatkan hubungan dengan koordinat ruang-waktu yang menunjukan bentuk baru dari topologi Lagrangian. Sifat invarian dari bentuk Pontryagin-Chern terhadap kuat medan tensor non-Abelian dan lemma Poincare dapat digunakan untuk mengkontruksi bentuk ChSAS yang menunjukan sifat quasi-invarian dibawah transformasi gauge. Artikel ini bertujuan untuk membuktikan bahwa kuat medan tensor Yang-Mills dari bentuk ChSAS memilik variasi gauge anomali non-Abelian seperti pada bentuk Chern-Simons. Integrasi bentuk ChSAS menghasilkan dimensi-4, 6 dan 8 variasi gauge genap dan memperlihatkan hubungan dengan bentuk Chern-Simons dimensi-3 dan 5 untuk variasi gauge ganjil. Bentuk ChSAS memperlihatkan variabel lebih kompleks yang menujukan sifat berosilasi. Tensors field strength transformation homogeneously to extend gauge transformation fulfilling charateristic gauge invariant form. Analysis gauge invariant in integral form shows corresponding with space-time coordinate that prove new topology Lagrangians form. Furthermore invariant charateristic of Pontryagin-Chern to non-Abelian tensor gauge fields and lemma Poincare used to contruct ChSAS forms which shows quasi-inavriant under gauge transformation. This paper aims to prove Yang-Mills tensor gauge field of ChSAS forms has variation non-Abelian anomaly like Chern-Simons forms. The integration ChSAS forms resulted 4, 6 and 8-dimensional even gauge variation which also correspond 3 and 5-dimensional odd gauge variation Chern-Simons forms. The ChSAS forms also showed complex variable and osilation. Keywords: Pontryagin-Chern, Kuat medan tensor non-Abelian, Chern-Simans-Antoniadis-Savvidy, Anomali Non-Abelian.

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5

Zanelli, Jorge. "Chern–Simons forms in gravitation theories." Classical and Quantum Gravity 29, no. 13 (May 25, 2012): 133001. http://dx.doi.org/10.1088/0264-9381/29/13/133001.

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6

Tradler, Thomas, Scott O. Wilson, and Mahmoud Zeinalian. "An elementary differential extension of odd K-theory." Journal of K-Theory 12, no. 2 (April 4, 2013): 331–61. http://dx.doi.org/10.1017/is013002018jkt218.

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AbstractThere is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This construction is functorial, and defines a differential extension of odd K-theory, fitting into natural commutative diagrams and exact sequences involving K-theory and differential forms. To prove this we obtain along the way several results concerning even and odd Chern and Chern-Simons forms.

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7

Green, Michael B. "Super-translations, superstrings and Chern-Simons forms." Physics Letters B 223, no. 2 (June 1989): 157–64. http://dx.doi.org/10.1016/0370-2693(89)90233-5.

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8

Bartocci, Claudio, Ugo Bruzzo, and Giovanni Landi. "Chern–Simons forms on principal superfiber bundles." Journal of Mathematical Physics 31, no. 1 (January 1990): 45–54. http://dx.doi.org/10.1063/1.528826.

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9

de Azcárraga, J. A., A. J. Macfarlane, and J. C. Pérez Bueno. "Effective actions, relative cohomology and Chern-Simons forms." Physics Letters B 419, no. 1-4 (February 1998): 186–94. http://dx.doi.org/10.1016/s0370-2693(97)01434-2.

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10

Izaurieta, F., P. Salgado, and S. Salgado. "Chern–Simons–Antoniadis–Savvidy forms and standard supergravity." Physics Letters B 767 (April 2017): 360–65. http://dx.doi.org/10.1016/j.physletb.2017.02.016.

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11

Cronström, C., Prem P. Srivastava, and K. Tanaka. "Self-Duality Condition and Critical Potentials." Zeitschrift für Naturforschung A 52, no. 1-2 (February 1, 1997): 147–48. http://dx.doi.org/10.1515/zna-1997-1-238.

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Abstract It is shown that the self-duality constraint on the scalar field (combined with the equations of motion) by itself leads to the critical forms for the potential that minimizes the energy functional in the Chern-Simons-Higgs (CSH) system. If we have only the Chern-Simons (CS) term in the SL (2, R) gauge group one obtains a formalism that yields the equations of motion of a variety on non-linear models in two dimensions when the curvature is set equal to zero.

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12

ANTONIADIS, IGNATIOS, and GEORGE SAVVIDY. "EXTENSION OF CHERN–SIMONS FORMS AND NEW GAUGE ANOMALIES." International Journal of Modern Physics A 29, no. 03n04 (February 10, 2014): 1450027. http://dx.doi.org/10.1142/s0217751x14500274.

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We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher-rank field-strength tensors. The integrals of these forms over the corresponding space–time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern–Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions.

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13

Robinson, D. C. "Generalized forms, Chern–Simons and Einstein–Yang–Mills theory." Classical and Quantum Gravity 26, no. 7 (March 23, 2009): 075019. http://dx.doi.org/10.1088/0264-9381/26/7/075019.

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14

Mora, Pablo, Rodrigo Olea, Ricardo Troncoso, and Jorge Zanelli. "Transgression forms and extensions of Chern-Simons gauge theories." Journal of High Energy Physics 2006, no. 02 (February 28, 2006): 067. http://dx.doi.org/10.1088/1126-6708/2006/02/067.

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15

Johnson, David L. "Chern–Simons forms on associated bundles, and boundary terms." Geometriae Dedicata 128, no. 1 (August 31, 2007): 39–54. http://dx.doi.org/10.1007/s10711-007-9182-4.

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16

Chen, Qingtao, and Fei Han. "Elliptic genera, transgression and loop space Chern-Simons forms." Communications in Analysis and Geometry 17, no. 1 (2009): 73–106. http://dx.doi.org/10.4310/cag.2009.v17.n1.a4.

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17

Gadea, P. M., and J. A. Oubiña. "Chern-Simons Forms Associated to Homogeneous Pseudo-Riemannian Structures." Rocky Mountain Journal of Mathematics 35, no. 1 (February 2005): 149–62. http://dx.doi.org/10.1216/rmjm/1181069772.

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18

Catalán, P., F. Izaurieta, P. Salgado, and S. Salgado. "Topological gravity and Chern–Simons forms in d = 4." Physics Letters B 751 (December 2015): 205–8. http://dx.doi.org/10.1016/j.physletb.2015.10.030.

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19

Berthomieu, Alain. "A version of smooth K-theory adapted to the total Chern class." Journal of K-Theory 6, no. 2 (October 2010): 197–230. http://dx.doi.org/10.1017/is010009026jkt104.

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AbstractA new model of smooth K0-theory ([5] [1]) is constructed, with the help of the total Chern class (contrary to the theories considered in ]1], [5], [12] and [13] which use the Chern character). The correspondence with the earlier model [1] is obtained by adapting, at the level of transgression forms, the usual formulae which express the Chern character in terms of the Chern classes and vice versa.The advantage of this new model is that it allows constructing Chern classes with values in integral Chern-Simons characters in a natural way: this construction answers a question asked by U. Bunke [4].

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20

Dupont, Johan L., and Flemming Lindblad Johansen. "Remarks on Determinant Line Bundles, Chern-Simons Forms and Invariants." MATHEMATICA SCANDINAVICA 91, no. 1 (September 1, 2002): 5. http://dx.doi.org/10.7146/math.scand.a-14376.

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We study generalized determinant line bundles for families of principal bundles and connections. We explore the connections of this line bundle and give conditions for the uniqueness of such. Furthermore we construct for families of bundles and connections over manifolds with boundary, a generalized Chern-Simons invariant as a section of a determinant line bundle.

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21

Babourova, O. V., and B. N. Frolov. "Pontryagin, Euler Forms and Chern–Simons Terms in Weyl–Cartan Space." Modern Physics Letters A 12, no. 17 (June 7, 1997): 1267–74. http://dx.doi.org/10.1142/s0217732397001278.

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The existence of the Pontryagin and Euler forms in a Weyl–Cartan space on the basis of the variational method with Lagrange multipliers are established. It is proved that these forms can be expressed via the exterior derivatives of the corresponding Chern–Simons terms in a Weyl–Cartan space with torsion and nonmetricity.

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22

Gadea, P. M., and J. A. Oubiña. "Chern-Simons forms of pseudo-Riemannian homogeneity on the oscillator group." International Journal of Mathematics and Mathematical Sciences 2003, no. 47 (2003): 3007–14. http://dx.doi.org/10.1155/s0161171203210164.

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We consider forms of Chern-Simons type associated to homogeneous pseudo-Riemannian structures. The corresponding secondary classes are a measure of the lack of a homogeneous pseudo-Riemannian space to be locally symmetric. In the present paper, we compute these forms for the oscillator group and the corresponding secondary classes of the compact quotients of this group.

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23

CECOTTI, S., S. FERRARA, and M. VILLASANTE. "LINEAR MULTIPLETS AND SUPER CHERN-SIMONS FORMS IN 4D-SUPERGRAVITY." International Journal of Modern Physics A 02, no. 06 (December 1987): 1839–69. http://dx.doi.org/10.1142/s0217751x8700096x.

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We explore general properties of matter coupled supergravities with antisymmetric tensor fields embedded in linear multiplets. The four-dimensional supersymmetric version of the Green-Schwarz mechanism leads to the introduction of super Chern-Simons form multiplets whose general component expressions are derived. The use of superconformal techniques allows us to discuss several topics relevant to superstring effective actions and in particular to give simple forms for the string-loop corrections to the Kahler potential and the U(1) anomaly cancelling term present in certain superstring compactifications.

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24

Blažić, Novica, Neda Bokan, and Peter B. Gilkey. "Pontrjagin forms, Chern Simons classes, Codazzi transformations, and affine hypersurfaces." Journal of Geometry and Physics 27, no. 3-4 (September 1998): 333–49. http://dx.doi.org/10.1016/s0393-0440(98)00005-9.

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25

Girardi, G., and R. Grimm. "Chern-Simons forms and four-dimensional N = 1 superspace geometry." Nuclear Physics B 292 (January 1987): 181–200. http://dx.doi.org/10.1016/0550-3213(87)90641-9.

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26

Eliezer, D., and G. W. Semenoff. "Intersection forms and the geometry of lattice Chern-Simons theory." Physics Letters B 286, no. 1-2 (July 1992): 118–24. http://dx.doi.org/10.1016/0370-2693(92)90168-4.

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27

Dixon, J. A., and M. J. Duff. "Chern-Simons forms, Mickelsson-Faddeev algebras and the p-branes." Physics Letters B 296, no. 1-2 (December 1992): 28–32. http://dx.doi.org/10.1016/0370-2693(92)90799-a.

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28

Verwimp, Theo. "Boundary terms in Lovelock gravity from dimensionally continued Chern–Simons forms." Journal of Mathematical Physics 33, no. 4 (April 1992): 1431–36. http://dx.doi.org/10.1063/1.529719.

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29

Hou, Shaoqi, Tao Zhu, and Zong-Hong Zhu. "Conserved charges in Chern-Simons modified theory and memory effects." Journal of Cosmology and Astroparticle Physics 2022, no. 04 (April 1, 2022): 032. http://dx.doi.org/10.1088/1475-7516/2022/04/032.

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Abstract In this work, conserved charges and fluxes at the future null infinity are determined in the asymptotically flat spacetime for Chern-Simons modified gravity. The flux-balance laws are used to constrain the memory effects. For tensor memories, the Penrose's conformal completion method is used to analyze the asymptotic structures and asymptotic symmetries, and then, conserved charges for the Bondi-Metzner-Sachs algebra are constructed with the Wald-Zoupas formalism. These charges take very similar forms to those in Brans-Dicke theory. For the scalar memory, Chern-Simons modified gravity is rewritten in the first-order formalism, and the scalar field is replaced by a 2-form field dual to it. With this dual formalism, the scalar memory is described by the vacuum transition induced by the large gauge transformation of the 2-form field.

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30

Zanelli, Jorge. "Chern–Simons forms and transgression actions or the universe as a subsystem." Journal of Physics: Conference Series 68 (May 1, 2007): 012002. http://dx.doi.org/10.1088/1742-6596/68/1/012002.

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31

GRIMM, RICHARD, MAXIMILIAN HASLER, and CARL HERRMANN. "THE N=2 VECTOR–TENSOR MULTIPLET, CENTRAL CHARGE SUPERSPACE, AND CHERN–SIMONS COUPLINGS." International Journal of Modern Physics A 13, no. 11 (April 30, 1998): 1805–16. http://dx.doi.org/10.1142/s0217751x98000792.

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We present a new, alternative interpretation of the vector–tensor multiplet as a two-form in central charge superspace. This approach provides a geometric description of the (nontrivial) central charge transformations ab initio and is naturally generalized to include couplings of Chern–Simons forms to the antisymmetric tensor gauge field, giving rise to a N=2 supersymmetric version of the Green–Schwarz anomaly cancellation mechanism.

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32

Maeda, Yoshiaki, Steven Rosenberg, and Fabián Torres-Ardila. "The geometry of loop spaces I: Hs-Riemannian metrics." International Journal of Mathematics 26, no. 04 (April 2015): 1540002. http://dx.doi.org/10.1142/s0129167x15400029.

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A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms, which take values in pseudodifferential operators (ΨDOs). These calculations are used in the followup paper [10] to construct Chern–Simons classes on TLM which detect nontrivial elements in the diffeomorphism group of certain Sasakian 5-manifolds associated to Kähler surfaces.

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33

Awada, M., and P. K. Townsend. "GaugedN=4,d=6 Maxwell-Einstein supergravity and ‘‘antisymmetric-tensor Chern-Simons’’ forms." Physical Review D 33, no. 6 (March 15, 1986): 1557–62. http://dx.doi.org/10.1103/physrevd.33.1557.

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34

NISSIMOV, E., S. PACHEVA, and S. SOLOMON. "ACTION PRINCIPLE FOR OVERDETERMINED SYSTEMS OF NONLINEAR FIELD EQUATIONS." International Journal of Modern Physics A 04, no. 03 (February 1989): 737–52. http://dx.doi.org/10.1142/s0217751x89000352.

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We propose a general scheme for constructing an action principle for arbitrary consistent overdetermined systems of nonlinear field equations. The principal tool is the BFV-BRST formalism. There is no need for star-product nor Chern-Simons forms. The main application of this general construction is the derivation of a superspace action in terms of unconstrained superfields for the D = 10N = 1 Super-Yang-Mills theory. The latter contains cubic as well as quartic interactions.

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35

GATES, S. JAMES, and J. W. DURACHTA. "GAUGE TWO-FORM IN D=4, N=4 SUPERGEOMETRY WITH SU(4) SUPERSYMMETRY." Modern Physics Letters A 04, no. 21 (October 20, 1989): 2007–16. http://dx.doi.org/10.1142/s0217732389002264.

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We employ a gauge two-form [Formula: see text] in place of the pseudoscalar B' to produce a version of on-shell D=4, N=4 superspace supergravity with SU(4) symmetry. The replacement is accomplished using the Chern-Simons forms associated with the six spin-1 fields of N=4 supergravity. Finally, a Green-Schwarz action is presented and the relation of the theory to the N=4, D=4 heterotic string is exhibited.

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36

EDELSTEIN, JOSÉ D., ALAN GARBARZ, OLIVERA MIŠKOVIĆ, and JORGE ZANELLI. "NAKED SINGULARITIES, TOPOLOGICAL DEFECTS AND BRANE COUPLINGS." International Journal of Modern Physics D 20, no. 05 (May 20, 2011): 839–49. http://dx.doi.org/10.1142/s0218271811019177.

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A conical defect in 2 + 1 anti-de Sitter space is a BTZ solution with a negative mass parameter. This is a naked singularity, but a rather harmless one: it is a point particle. Naturally, the energy density and the spacetime curvature have a δ-like singularity at the conical defect, but that does not give rise to any unphysical situations. Since the conical solution implies the presence of a source, applying reverse enginnering, one can identify the coupling term that is required in the action to account for that source. In that way, a relation is established between the identification operation that gives rise to the topological defect and the interaction term in the action that produces it. This idea has a natural extension to higher dimensions, where instead of a point particle (zero-brane) one finds membranes of even spatial dimensions (p-branes, with p = 2n). The generalization to other abelian and nonabelian gauge theories — including (super-) gravities — is fairly straightforward: the 2n-brane couples to a (2n + 1) Chern–Simons form. The construction suggests a generic role for Chern–Simons forms as the natural way to couple a gauge connection to a brane and avoids the inconsistency that results from the minimal coupling between a brane and a fundamental p-form field.

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37

KAWAMOTO, NOBORU, HIROSHI UMETSU, and TAKUYA TSUKIOKA. "GENERALIZED GAUGE THEORIES AND THE WEINBERG–SALAM MODEL WITH DIRAC–KÄHLER FERMIONS." International Journal of Modern Physics A 16, no. 23 (September 20, 2001): 3867–95. http://dx.doi.org/10.1142/s0217751x01004438.

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We extend the previously proposed generalized gauge theory formulation of the Chern–Simons type and topological Yang–Mills type actions into Yang–Mills type actions. We formulate gauge fields and Dirac–Kähler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one-form gauge fields accommodated with the graded Lie algebra of SU (2|1) supergroup leads the Weinberg–Salam model. Thus the Weinberg–Salam model formulated by noncommutative geometry is a particular example of the present formulation.

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38

EZAWA, KIYOSHI. "TRANSITION AMPLITUDE IN (2+1)-DIMENSIONAL CHERN-SIMONS GRAVITY ON A TORUS." International Journal of Modern Physics A 09, no. 27 (October 30, 1994): 4727–45. http://dx.doi.org/10.1142/s0217751x94001898.

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In the framework of the Chern-Simons gravity proposed by Witten, a transition amplitude of a torus universe in (2+1)-dimensional quantum gravity is computed. This amplitude has the desired properties as a probability amplitude of the quantum mechanics of a torus universe, namely, it has a peak on the “classical orbit” and it satisfies the Schrödinger equation of the (2+1)-dimensional gravity. The discussion is given that the classical orbit dominance of the amplitude is not altered by taking the modular invariance into account and that this amplitude can serve as a covariant transition amplitude in a particular sense. A set of the modular-covariant wave functions is also constructed and they are shown to be equivalent to the weight-½ Maass forms.

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39

AHN, CHANGHYUN, and KYUNGSUNG WOO. "ARE THERE ANY NEW VACUA OF GAUGED ${\mathcal N}=8$ SUPERGRAVITY IN FOUR DIMENSIONS?" International Journal of Modern Physics A 25, no. 09 (April 10, 2010): 1819–51. http://dx.doi.org/10.1142/s0217751x10048251.

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We consider the most general SU(3) singlet space of gauged [Formula: see text] supergravity in four dimensions. The SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms. By exponentiating these four-forms, we eventually obtain the new scalar potential. For the two extreme limits, we reproduce the previous results found by Warner in 1983. In particular, for the [Formula: see text] critical point, we find the constraint surface parametrized by three scalar fields on which the cosmological constant has the same value. We obtain the BPS domain-wall solutions for restricted scalar submanifold. We also describe the three-dimensional mass-deformed superconformal Chern–Simons matter theory dual to the above supersymmetric flows in four dimensions.

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40

D’AURIA, RICCARDO, PIETRO FRE’, GUIDO DE MATTEIS, and IGOR PESANDO. "SUPERSPACE CONSTRAINTS AND CHERN-SIMONS COHOMOLOGY IN D=4 SUPERSTRING EFFECTIVE THEORIES." International Journal of Modern Physics A 04, no. 14 (August 20, 1989): 3577–613. http://dx.doi.org/10.1142/s0217751x89001412.

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The linear multiplet, composed of the dilaton ϕ, of an antisymmetric gauge field Bμν and of a spinor χ is always present in any superstring induced N=1D=4 supergravity model. We consider its coupling to supergravity using only superspace Bianchi identities and the rheonomy approach. In this way, our results are fully general and independent from the choice of any Lagrangian, a concept which is never mentioned in this paper. We consider two situations corresponding to two different free differential algebras: (1) the case where there are no Chern-Simons terms in the Bμν field strength Hμνρ and (2) the case where such terms are included in Hμνρ. Case (2) is obviously the one chosen by string theory on the ground of anomaly cancellation. In both cases, we must solve the H-Bianchi identity using a solution of the super Poincare’ Bianchi identities as a background. Such a solution, besides the physical fields displays a certain number of auxiliary fields. The most general solution of the super Poincare’ Bianchis we have to consider corresponds to 16⊕16 off-shell multiplet which, by suitable choices can be reduced either to the so-called old minimal or to the new minimal 12⊕12 multiplet. We give the general solution of the H-Bianchi within the 16⊕16 formulation both with and without Chern-Simons terms. This is done through the D=4 analogue of Bonora-Pasti-Tonin theorem of the 10D anomaly free supergravity. By specializing our parameters, we obtain the form of the coupling in the new minimal model retrieving in this case the results of Cecotti, Ferrara and Villasante. In addition we clarify the geometrical meaning of R-symmetry showing that in the absence of Chern-Simons forms, the condition for the embedding of the linear multiplet into the Kaehler manifold [Formula: see text] spanned by the chiral multiplets (existence on [Formula: see text] of a U(1) Killing vector) is the same condition which guarantees the existence of a local Weyl transformation by means of which the 16⊕16 curvatures can be reduced to the new minimal form and the scalar complex scalar auxiliary field S can be set to zero. Finally, we discuss the arbitrariness contained in the solution of the H-Bianchi identities at the level of the (0, 3) superspace sector. We derive the D=4 analogue of the superspace cocycle which is responsible for the Grisaru-Zanon R4-terms in the D=10 case.

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41

de Azcárraga, J. A., J. M. Izquierdo, M. Picón, and O. Varela. "Generating Lie and gauge free differential (super)algebras by expanding Maurer–Cartan forms and Chern–Simons supergravity." Nuclear Physics B 662, no. 1-2 (July 2003): 185–219. http://dx.doi.org/10.1016/s0550-3213(03)00342-0.

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ROY, ASHIM KUMAR. "GAUGE AND SHAPE INDEPENDENCE OF FRACTIONAL SPIN OF DEFORMED SOLITONS IN THE (2+1)-DIMENSIONAL O(3) σ MODEL." International Journal of Modern Physics A 11, no. 04 (February 10, 1996): 759–75. http://dx.doi.org/10.1142/s0217751x96000353.

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The O(3) nonlinear σ model with the Hopf term and with a Chern–Simons gauge coupling in 2+1 dimensions is considered for an understanding of the soliton shape and gauge dependence of the fractional spin and statistics exhibited by the particle-like solutions. Some explicit forms of the shape-defining (for the deformed solitons of these models) functions and the adiabatic time-dependent function are used to assess the fractional spin. In two different gauges, a proper and explicit analysis shows that the fractional spin is a truly gauge- as well as shape-independent entity. This demonstrates that the fractional spin of solitons in the O(3) σ model is a topologically invariant quantity — a fact which has been put in doubt by some authors.

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ABOUELSAOOD, A., C. N. POPE, E. SEZGIN, and X. SHEN. "GAUGED SIGMA MODELS FROM 2 + 1 DIMENSIONS AND THE ISSUE OF UNITARITY." Modern Physics Letters A 05, no. 23 (September 20, 1990): 1841–50. http://dx.doi.org/10.1142/s0217732390002109.

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As a Lagrangian realization of the Goddard-Kent-Olive G/H coset construction, Castellani, D'Auria and Levi recently proposed a gauged Wess-Zumino-Witten model in which the topological term is a difference of Chern-Simons forms. We show that their Lagrangian is actually an ungauged Wess-Zumino-Witten model plus a gauge field coupled linearly to an H-current, thus describing non-abelian chiral bosons with a linear constraint. We carry out the Dirac quantization procedure and show that the Hamiltonian is of the current-current form with indefinite signature, thus signaling instability. We also clarify the relationship of this model with that of Moore and Seiberg, which does provide an anomaly-free formulation of the GKO coset construction.

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Ahmed, Nasr. "Ricci–Gauss–Bonnet holographic dark energy in Chern–Simons modified gravity: A flat FLRW quintessence-dominated universe." Modern Physics Letters A 35, no. 05 (October 11, 2019): 2050007. http://dx.doi.org/10.1142/s0217732320500078.

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We discuss the recently suggested Ricci–Gauss–Bonnet holographic dark energy in Chern–Simons modified gravity. We have tested some general forms of the scale factor [Formula: see text], and used two physically reasonable forms which have been proved to be consistent with observations. Both solutions predict a sign flipping in the evolution of cosmic pressure which is positive during the early-time deceleration and negative during the late-time acceleration. This sign flipping in the evolution of cosmic pressure helps in explaining the cosmic deceleration–acceleration transition, and it has appeared in other cosmological models in different contexts. However, this work shows a pressure singularity which needs to be explained. The evolution of the equation of state parameter [Formula: see text] shows the same asymptotic behavior for both solutions indicating a quintessence-dominated universe in the far future. We also note that [Formula: see text] goes to negative values (leaving the decelerating dust-dominated era at [Formula: see text]) at exactly the same time the pressure becomes negative. Again, there is another singularity in the behavior of [Formula: see text] which happens at the same cosmic time of the pressure singularity.

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Girardi, Georges, and Richard Grimm. "The Superspace Geometry of Gravitational Chern–Simons Forms and Their Couplings to Linear Multiplets: A Self-Contained Presentation." Annals of Physics 272, no. 1 (February 1999): 49–129. http://dx.doi.org/10.1006/aphy.1998.5880.

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BALACHANDRAN, A. P., and P. TEOTONIO-SOBRINHO. "VERTEX OPERATORS FOR THE BF SYSTEM AND ITS SPIN–STATISTICS THEOREMS." International Journal of Modern Physics A 09, no. 10 (April 20, 1994): 1569–629. http://dx.doi.org/10.1142/s0217751x94000704.

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Let B and [Formula: see text] be two-forms, Fµν being the field strength of an Abelian connection A. The topological BF system is given by the integral of B ∧ F. With "kinetic energy" terms added for B and A, it generates a mass for A, thereby suggesting an alternative to the Higgs mechanism, and also gives the London equations. The BF action, being the large length and time scale limit of this augmented action, is thus of physical interest. In earlier work, it has been studied on spatial manifolds Σ with boundaries ∂Σ, and the existence of edge states localized at ∂Σ has been established. They are analogous to the conformal family of edge states to be found in a Chern–Simons theory in a disc. Here we introduce charges and vortices (thin flux tubes) as sources in the BF system and show that they acquire an infinite number of spin excitations due to renormalization, just as a charge coupled to a Chern–Simons potential acquires a conformal family of spin excitations. For a vortex, these spins are transverse and attached to each of its points, so that it resembles a ribbon. Vertex operators for the creation of these sources are constructed and interpreted in terms of a Wilson integral involving A and a similar integral involving B. The standard spin–statistics theorem is proved for these sources. A new spin–statistics theorem, showing the equality of the "interchange" of two identical vortex loops and 2π rotation of the transverse spins of a constituent vortex, is established. Aharonov–Bohm interactions of charges and vortices are studied. The existence of topologically nontrivial vortex spins is pointed out and their vertex operators are also discussed.

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Frodden, Ernesto, and Diego Hidalgo. "Surface charges toolkit for gravity." International Journal of Modern Physics D 29, no. 06 (April 2020): 2050040. http://dx.doi.org/10.1142/s0218271820500406.

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These notes provide a detailed catalog of surface charge formulas for different classes of gravity theories. The present catalog reviews and extends the existing literature on the topic. Part of the focus is on reviewing the method to compute quasi-local surface charges for gauge theories in order to clarify conceptual issues and their range of applicability. Many surface charge formulas for gravity theories are expressed in metric, tetrads-connection, Chern–Simons connection, and even BF variables. For most of them, the language of differential forms is exploited and contrasted with the more popular metric components language. The gravity theory is coupled with matter fields as scalar, Maxwell, Skyrme, Yang–Mills, and spinors. Furthermore, three examples with ready-to-download notebook codes, show the method in full action. Several new results are highlighted through the notes.

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BRANSON, THOMAS, and A. ROD GOVER. "PONTRJAGIN FORMS AND INVARIANT OBJECTS RELATED TO THE Q-CURVATURE." Communications in Contemporary Mathematics 09, no. 03 (June 2007): 335–58. http://dx.doi.org/10.1142/s0219199707002460.

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It was shown by Chern and Simons that the Pontrjagin forms are conformally invariant. We show them to be the Pontrjagin forms of the conformally invariant tractor connection. The Q-curvature is intimately related to the Pfaffian. Working on even-dimensional manifolds, we show how the k-form operators Qk of [12], which generalize the Q-curvature, retain a key aspect of the Q-curvature's relation to the Pfaffian, by obstructing certain representations of natural operators on closed forms. In a closely related direction, we show that the Qk give rise to conformally invariant quadratic forms Θk on cohomology that interpolate, in a suitable sense, between the integrated metric pairing (at k = n/2) and the Pfaffian (at k = 0). Using a different construction, we show that the Qk operators yield a map from conformal structures to Lagrangian subspaces of the direct sum Hk ⊕ Hk (where Hk is the dual of the de Rham cohomology space Hk); in an appropriate sense this generalizes the period map. We couple the Qk operators with the Pontrjagin forms to construct new natural densities that have many properties in common with the original Q-curvature; in particular these integrate to global conformal invariants. We also work out a relevant example, and show that the proof of the invariance of the (nonlinear) action functional whose critical metrics have constant Q-curvature extends to the action functionals for these new Q-like objects. Finally we set up eigenvalue problems that generalize to Qk-operators the Q-curvature prescription problem.

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BOI, LUCIANO. "IDEAS OF GEOMETRIZATION, GEOMETRIC INVARIANTS OF LOW-DIMENSIONAL MANIFOLDS, AND TOPOLOGICAL QUANTUM FIELD THEORIES." International Journal of Geometric Methods in Modern Physics 06, no. 05 (August 2009): 701–57. http://dx.doi.org/10.1142/s0219887809003783.

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The aim of the first part of this paper is to make some reflections on the role of geometrical and topological concepts in the developments of theoretical physics, especially in gauge theory and string theory, and we show the great significance of these concepts for a better understanding of the dynamics of physics. We will claim that physical phenomena essentially emerge from the geometrical and topological structure of space–time. The attempts to solve one of the central problems in 20th theoretical physics, i.e. how to combine gravity and the other forces into an unitary theoretical explanation of the physical world, essentially depends on the possibility of building a new geometrical framework conceptually richer than Riemannian geometry. In fact, it still plays a fundamental role in non-Abelian gauge theories and in superstring theory, thanks to which a great variety of new mathematical structures has emerged. The scope of this presentation is to highlight the importance of these mathematical structures for theoretical physics. A very interesting hypothesis is that the global topological properties of the manifold's model of space–time play a major role in quantum field theory (QFT) and that, consequently, several physical quantum effects arise from the nonlocal changing metrical and topological structure of these manifold. Thus the unification of general relativity and quantum theory require some fundamental breakthrough in our understanding of the relationship between space–time and quantum process. In particular the superstring theories lead to the guess that the usual structure of space–time at the quantum scale must be dropped out from physical thought. Non-Abelian gauge theories satisfy the basic physical requirements pertaining to the symmetries of particle physics because they are geometric in character. They profoundly elucidate the fundamental role played by bundles, connections, and curvature in explaining the essential laws of nature. Kaluza–Klein theories and more remarkably superstring theory showed that space–time symmetries and internal (quantum) symmetries might be unified through the introduction of new structures of space with a different topology. This essentially means, in our view, that "hidden" symmetries of fundamental physics can be related to the phenomenon of topological change of certain class of (presumably) nonsmooth manifolds. In the second part of this paper, we address the subject of topological quantum field theories (TQFTs), which constitute a remarkably important meeting ground for physicists and mathematicians. TQFTs can be used as a powerful tool to probe geometry and topology in low dimensions. Chern–Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of QFTs which can be exactly (nonperturbatively) and explicitly solved. Abelian Chern–Simons theory provides a field theoretic interpretation of the linking and self-linking numbers of a link (i.e. the union of a finite number of disjoint knots). In non-Abelian theories, vacuum expectation values of Wilson link operators yield a class of polynomial link invariants; the simplest of them is the well-known Jones polynomial. Powerful methods for complete analytical and nonperturbative computation of these knot and link invariants have been developed. From these invariants for unoriented and framed links in S3, an invariant for any three-manifold can be easily constructed by exploiting the Lickorish–Wallace surgery presentation of three-manifolds. This invariant up to a normalization is the partition function of the Chern–Simons field theory. Even perturbative analysis of Chern–Simons theories are rich in their mathematical structure; these provide a field theoretic interpretation of Vassiliev knot invariants. In Donaldson–Witten theory perturbative methods have proved their relations to Donaldson invariants. Nonperturbative methods have been applied after the work by Seiberg and Witten on N = 2 supersymmetric Yang–Mills theory. The outcome of this application is a totally unexpected relation between Donaldson invariants and a new set of topological invariants called Seiberg–Witten invariants. Not only in mathematics, Chern–Simons theories find important applications in three- and four-dimensional quantum gravity also. Work on TQFT suggests that a quantum gravity theory can be formulated in three-dimensional space–time. Attempts have been made in the last years to formulate a theory of quantum gravity in four-dimensional space–time using "spin networks" and "spin foams". More generally, the developments of TQFTs represent a sort of renaissance in the relation between geometry and physics. The most important (new) feature of present developments is that links are being established between quantum physics and topology. Maybe this link essentially rests on the fact that both quantum theory and topology are characterized by discrete phenomena emerging from a continuous background. One very interesting example is the super-symmetric quantum mechanics theory, which has a deep geometric meaning. In the Witten super-symmetric quantum mechanics theory, where the Hamiltonian is just the Hodge–Laplacian (whereas the quantum Hamiltonian corresponding to a classical particle moving on a Riemannian manifold is just the Laplace–Beltrami differential operator), differential forms are bosons or fermions depending on the parity of their degrees. Witten went to introduce a modified Hodge–Laplacian, depending on a real-valued function f. He was then able to derive the Morse theory (relating critical points of f to the Betti numbers of the manifold) by using the standard limiting procedures relating the quantum and classical theories. Super-symmetric QFTs essentially should be viewed as the differential geometry of certain infinite-dimensional manifolds, including the associated analysis (e.g. Hodge theory) and topology (e.g. Betti numbers). A further comment is that the QFTs of interest are inherently nonlinear, but the nonlinearities have a natural origin, e.g. coming from non-Abelian Lie groups. Moreover there is usually some scaling or coupling parameter in the theory which in the limit relates to the classical theory. Fundamental topological aspects of such a quantum theory should be independent of the parameters and it is therefore reasonable to expect them to be computable (in some sense) by examining the classical limit. This means that such topological information is essentially robust and should be independent of the fine analytical details (and difficulties) of the full quantum theory. In the last decade much effort has been done to use these QFTs as a conceptual tool to suggest new mathematical results. In particular, they have led to spectacular progress in our understanding of geometry in low dimensions. It is most likely no accident that the usual QFTs can only be renormalized in (space–time) dimensions ≤4, and this is precisely the range in which difficult phenomena arise leading to deep and beautiful theories (e.g. the work of Thurston in three dimensions and Donaldson in four dimensions). It now seems clear that the way to investigate the subtleties of low-dimensional manifolds is to associate to them suitable infinite-dimensional manifolds (e.g. spaces of connections) and to study these by standard linear methods (homology, etc.). In other words we use QFT as a refined tool to study low-dimensional manifolds.

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Odintsov, Sergei D., Vasilis K. Oikonomou, and Ratbay Myrzakulov. "Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview." Symmetry 14, no. 4 (April 3, 2022): 729. http://dx.doi.org/10.3390/sym14040729.

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In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects of neutrinos on primordial gravitational waves. With this short review, our main aim is to gather all the necessary information for studying the effects of modified gravity on primordial gravitational waves in a concrete and quantitative way and in a single paper. After reviewing all the necessary techniques for extracting the general relativistic energy spectrum, and how to obtain, in a WKB way, the modified gravity damping or amplifying factor, we concentrate on specific forms of modified gravity of interest. The most important parameter involved for the calculation of the effects of modified gravity on the energy spectrum is the parameter aM, which we calculate for the cases of f(R,ϕ) gravity, Chern–Simons-corrected f(R,ϕ) gravity, Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity. The exact form of aM is presented explicitly for the first time in the literature. With regard to Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity theories, we focus on the case in which the gravitational wave propagating speed is equal to that of light in a vacuum. We provide expressions for aM expressed in terms of the cosmic time and in terms of the redshift, which can be used directly for the numerical calculation of the effect of modified gravity on the primordial gravitational wave energy spectrum.

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