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Статті в журналах з теми "Bundle gerbes"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

SZAMOTULSKI, MARCIN, and DOROTA MARCINIAK. "TOTAL SPACE OF ABELIAN GERBES." International Journal of Modern Physics A 24, no. 15 (June 20, 2009): 2877–88. http://dx.doi.org/10.1142/s0217751x09046229.

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Анотація:

We present a generalization of the construction of a principal G-bundle from a one Čech cocycle to the case of higher abelian gerbes. We prove that the sheaf of local sections of the associated bundle to a higher abelian gerbe is isomorphic to the sheaf of sections of the gerbe itself. Our main result states that equivalence classes of higher abelian gerbes are in bijection with isomorphism classes of the corresponding bundles. We also present topological characterization of those bundles. In the last section, we show that the usual notion of Ehresmann connection leads to the gerbe connection for higher ℂ*-gerbes.

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2

JURČO, BRANISLAV. "CROSSED MODULE BUNDLE GERBES; CLASSIFICATION, STRING GROUP AND DIFFERENTIAL GEOMETRY." International Journal of Geometric Methods in Modern Physics 08, no. 05 (August 2011): 1079–95. http://dx.doi.org/10.1142/s0219887811005555.

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We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to a (Lie) crossed module (H → D) there is a simplicial group [Formula: see text], the nerve of the groupoid [Formula: see text] defined by the crossed module, and its geometric realization, the topological group [Formula: see text]. We introduce crossed module bundle gerbes so that their (stable) equivalence classes are in a bijection with equivalence classes of principal [Formula: see text]-bundles. We discuss the string group and string structures from this point of view. Also, we give a simplicial interpretation to the bundle gerbe connection and bundle gerbe B-field.

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3

Bunk, Severin. "Gerbes in Geometry, Field Theory, and Quantisation." Complex Manifolds 8, no. 1 (January 1, 2021): 150–82. http://dx.doi.org/10.1515/coma-2020-0112.

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Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms of differential cohomology. We then survey how the surface holonomy of bundle gerbes combines with their transgression line bundles to yield a smooth bordism-type field theory. Finally, we exhibit the use of bundle gerbes in geometric quantisation of 2-plectic as well as 1- and 2-shifted symplectic forms. This generalises earlier applications of gerbes to the prequantisation of quasi-symplectic groupoids.

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4

Murray, M. K. "Bundle Gerbes." Journal of the London Mathematical Society 54, no. 2 (October 1996): 403–16. http://dx.doi.org/10.1112/jlms/54.2.403.

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5

JURČO, BRANISLAV. "NONABELIAN BUNDLE 2-GERBES." International Journal of Geometric Methods in Modern Physics 08, no. 01 (February 2011): 49–78. http://dx.doi.org/10.1142/s0219887811004963.

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Анотація:

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. If (L → M → N) is a Lie 2-crossed module and Y → X is a surjective submersion then an (L → M → N)-bundle 2-gerbe over X is defined in terms of a so-called (L → M → N)-bundle gerbe over the fiber product Y[2] = Y × XY, which is an (L → M)-bundle gerbe over Y[2] equipped with a trivialization under the change of its structure crossed module from L → M to 1 → N, and which is subjected to further conditions on higher fiber products Y[3], Y[4] and Y[5]. String structures can be described and classified using 2-crossed module bundle 2-gerbes.

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6

Stevenson, Daniel. "Bundle 2-Gerbes." Proceedings of the London Mathematical Society 88, no. 02 (March 2004): 405–35. http://dx.doi.org/10.1112/s0024611503014357.

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7

Murray, Michael K., David Michael Roberts, Danny Stevenson, and Raymond F. Vozzo. "Equivariant bundle gerbes." Advances in Theoretical and Mathematical Physics 21, no. 4 (2017): 921–75. http://dx.doi.org/10.4310/atmp.2017.v21.n4.a3.

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8

Bunk, Severin, Christian Sämann, and Richard J. Szabo. "The 2-Hilbert space of a prequantum bundle gerbe." Reviews in Mathematical Physics 30, no. 01 (January 10, 2018): 1850001. http://dx.doi.org/10.1142/s0129055x18500010.

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We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier–Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf’s version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantization. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant–Souriau prequantization in this setting, including its dimensional reduction to ordinary prequantization.

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9

Bunk, Severin, Lukas Müller, and Richard J. Szabo. "Smooth 2-Group Extensions and Symmetries of Bundle Gerbes." Communications in Mathematical Physics 384, no. 3 (May 25, 2021): 1829–911. http://dx.doi.org/10.1007/s00220-021-04099-7.

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AbstractWe study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line bundles on M. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev–Mickelsson–Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-group models within our geometric framework. Starting from a basic gerbe on a compact simply-connected Lie group G, we prove that the smooth 2-group extensions of G arising from our construction provide new models for the string group of G.

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10

MURRAY, MICHAEL K., and RAYMOND F. VOZZO. "CIRCLE ACTIONS, CENTRAL EXTENSIONS AND STRING STRUCTURES." International Journal of Geometric Methods in Modern Physics 07, no. 06 (September 2010): 1065–92. http://dx.doi.org/10.1142/s0219887810004725.

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The caloron correspondence can be understood as an equivalence of categories between G-bundles over circle bundles and LG ⋊ρ S1-bundles where LG is the group of smooth loops in G. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an LG ⋊ρ S1-bundle.

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11

Gawędzki, Krzysztof. "Bundle gerbes for topological insulators." Banach Center Publications 114 (2018): 145–80. http://dx.doi.org/10.4064/bc114-4.

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12

Bouwknegt, Peter, Varghese Mathai, and Siye Wu. "Bundle gerbes and moduli spaces." Journal of Geometry and Physics 62, no. 1 (January 2012): 1–10. http://dx.doi.org/10.1016/j.geomphys.2011.08.005.

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13

Carey, A. L., and M. K. Murray. "Faddeev's anomaly and bundle gerbes." Letters in Mathematical Physics 37, no. 1 (May 1996): 29–36. http://dx.doi.org/10.1007/bf00400136.

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14

Waldorf, Konrad. "Multiplicative bundle gerbes with connection." Differential Geometry and its Applications 28, no. 3 (June 2010): 313–40. http://dx.doi.org/10.1016/j.difgeo.2009.10.006.

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15

Bunke, Ulrich, and Thomas Nikolaus. "T-duality via gerby geometry and reductions." Reviews in Mathematical Physics 27, no. 05 (June 2015): 1550013. http://dx.doi.org/10.1142/s0129055x15500130.

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Анотація:

We consider topological T-duality of torus bundles equipped with [Formula: see text]-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S1-valued functions which are constant along the torus fibers. We observe that such a reduction is exactly the additional datum needed for the construction of a T-dual pair. We illustrate the theory by working out the example of the canonical lifting gerbe on a compact Lie group which is a torus bundle over the associated flag manifold. It was a recent observation of Daenzer and van Erp [16] that for certain compact Lie groups and a particular choice of the gerbe, the T-dual torus bundle is given by the Langlands dual group.

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16

GAWȨDZKI, KRZYSZTOF, and NUNO REIS. "WZW BRANES AND GERBES." Reviews in Mathematical Physics 14, no. 12 (December 2002): 1281–334. http://dx.doi.org/10.1142/s0129055x02001557.

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Анотація:

We reconsider the role that bundle gerbes play in the formulation of the WZW model on closed and open surfaces. In particular, we show how an analysis of bundle gerbes on groups covered by SU(N) permits to determine the spectrum of symmetric branes in the boundary version of the WZW model with such groups as the target. We also describe a simple relation between the open string amplitudes in the WZW models based on simply connected groups and in their simple-current orbifolds.

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17

WALDORF, KONRAD. "A LOOP SPACE FORMULATION FOR GEOMETRIC LIFTING PROBLEMS." Journal of the Australian Mathematical Society 90, no. 1 (February 2011): 129–44. http://dx.doi.org/10.1017/s1446788711001182.

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AbstractWe review and then combine two aspects of the theory of bundle gerbes. The first concerns lifting bundle gerbes and connections on those, developed by Murray and by Gomi. Lifting gerbes represent obstructions against extending the structure group of a principal bundle. The second is the transgression of gerbes to loop spaces, initiated by Brylinski and McLaughlin and with recent contributions of the author. Combining these two aspects, we obtain a new formulation of lifting problems in terms of geometry on the loop space. Most prominently, our formulation explains the relation between (complex) spin structures on a Riemannian manifold and orientations of its loop space.

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18

Alfonsi, Luigi. "Towards an extended/higher correspondence." Complex Manifolds 8, no. 1 (January 1, 2021): 302–28. http://dx.doi.org/10.1515/coma-2020-0121.

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Abstract In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes. Double Field Theory is T-duality covariant formulation of the supergravity limit of String Theory, which generalises Kaluza-Klein theory by unifying metric and Kalb-Ramond field on a doubled-dimensional space. In light of the proposed correspondence, this doubled geometry is interpreted as an atlas description of the higher geometry of bundle gerbes. In this sense, Double Field Theory can be interpreted as a field theory living on the total space of the bundle gerbe, just like Kaluza-Klein theory is set on the total space of a principal bundle. This correspondence provides a higher geometric interpretation for para-Hermitian geometry which opens the door to its generalisation to Exceptional Field Theory. This review is based on, but not limited to, my talk at the workshop Generalized Geometry and Applications at Universität Hamburg on 3rd of March 2020.

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19

Krepski, Derek, and Jennifer Vaughan. "Multiplicative vector fields on bundle gerbes." Differential Geometry and its Applications 84 (October 2022): 101931. http://dx.doi.org/10.1016/j.difgeo.2022.101931.

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20

Becker, Kimberly E., Michael K. Murray, and Daniel Stevenson. "The Weyl map and bundle gerbes." Journal of Geometry and Physics 149 (March 2020): 103572. http://dx.doi.org/10.1016/j.geomphys.2019.103572.

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21

Gawędzki, Krzysztof, Rafał R. Suszek, and Konrad Waldorf. "Bundle gerbes for orientifold sigma models." Advances in Theoretical and Mathematical Physics 15, no. 3 (2011): 621–87. http://dx.doi.org/10.4310/atmp.2011.v15.n3.a1.

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22

Mathai, Varghese, and David Roberts. "Yang–Mills theory for bundle gerbes." Journal of Physics A: Mathematical and General 39, no. 20 (May 3, 2006): 6039–44. http://dx.doi.org/10.1088/0305-4470/39/20/027.

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23

CAREY, ALAN L., JOUKO MICKELSSON, and MICHAEL K. MURRAY. "BUNDLE GERBES APPLIED TO QUANTUM FIELD THEORY." Reviews in Mathematical Physics 12, no. 01 (January 2000): 65–90. http://dx.doi.org/10.1142/s0129055x00000046.

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This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah–Patodi–Singer index theory construction of the bundle of fermionic Fock spaces parameterized by vector potentials in odd space dimensions and a proof that this leads in a simple manner to the known Schwinger terms (Mickelsson–Faddeev cocycle) for the gauge group action. This gives an explicit computation of the Dixmier–Douady class of the associated bundle gerbe. The method also works in other cases of fermions in external fields (external gravitational field, for example) provided that the APS theorem can be applied; however, we have worked out the details only in the case of vector potentials. Another example, in which the bundle gerbe curvature plays a role, arises from the WZW model on Riemann surfaces. A further example is the "existence of string structures" question. We conclude by showing how global Hamiltonian anomalies fit within this framework.

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24

Murray, Michael K., and Daniel Stevenson. "Bundle Gerbes: Stable Isomorphism and Local Theory." Journal of the London Mathematical Society 62, no. 3 (December 2000): 925–37. http://dx.doi.org/10.1112/s0024610700001551.

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25

GOMI, KIYONORI. "CONNECTIONS AND CURVINGS ON LIFTING BUNDLE GERBES." Journal of the London Mathematical Society 67, no. 02 (March 24, 2003): 510–26. http://dx.doi.org/10.1112/s0024610702004076.

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26

Murray, Michael K., and Daniel Stevenson. "Higgs Fields, Bundle Gerbes and String Structures." Communications in Mathematical Physics 243, no. 3 (December 1, 2003): 541–55. http://dx.doi.org/10.1007/s00220-003-0984-4.

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27

Bunk, Severin, and Richard J. Szabo. "Fluxes, bundle gerbes and 2-Hilbert spaces." Letters in Mathematical Physics 107, no. 10 (May 23, 2017): 1877–918. http://dx.doi.org/10.1007/s11005-017-0971-x.

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28

MURRAY, MICHAEL, and DANNY STEVENSON. "A NOTE ON BUNDLE GERBES AND INFINITE-DIMENSIONALITY." Journal of the Australian Mathematical Society 90, no. 1 (February 2011): 81–92. http://dx.doi.org/10.1017/s1446788711001078.

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AbstractLet (P,Y ) be a bundle gerbe over a fibre bundle Y →M. We show that if M is simply connected and the fibres of Y →M are connected and finite-dimensional, then the Dixmier–Douady class of (P,Y ) is torsion. This corrects and extends an earlier result of the first author.

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29

Schreiber, Urs, Christoph Schweigert, and Konrad Waldorf. "Unoriented WZW Models and Holonomy of Bundle Gerbes." Communications in Mathematical Physics 274, no. 1 (June 13, 2007): 31–64. http://dx.doi.org/10.1007/s00220-007-0271-x.

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30

Hekmati, Pedram, Michael K. Murray, Richard J. Szabo, and Raymond F. Vozzo. "Real bundle gerbes, orientifolds and twisted $KR$-homology." Advances in Theoretical and Mathematical Physics 23, no. 8 (2019): 2093–159. http://dx.doi.org/10.4310/atmp.2019.v23.n8.a5.

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31

Carey, A. L., M. K. Murray, and B. L. Wang. "Higher bundle gerbes and cohomology classes in gauge theories." Journal of Geometry and Physics 21, no. 2 (January 1997): 183–97. http://dx.doi.org/10.1016/s0393-0440(96)00014-9.

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32

Bouwknegt, Peter, Alan L. Carey, Varghese Mathai, Michael K. Murray, and Danny Stevenson. "Twisted K-Theory and K-Theory of Bundle Gerbes." Communications in Mathematical Physics 228, no. 1 (June 1, 2002): 17–49. http://dx.doi.org/10.1007/s002200200646.

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33

Aschieri, Paolo, Luigi Cantini, and Branislav Jurčo. "Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory." Communications in Mathematical Physics 254, no. 2 (November 17, 2004): 367–400. http://dx.doi.org/10.1007/s00220-004-1220-6.

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34

Hekmati, Pedram, Michael K. Murray, Danny Stevenson, and Raymond F. Vozzo. "The Faddeev–Mickelsson–Shatashvili Anomaly and Lifting Bundle Gerbes." Communications in Mathematical Physics 319, no. 2 (November 17, 2012): 379–93. http://dx.doi.org/10.1007/s00220-012-1608-7.

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35

Carey, Alan L., Stuart Johnson, Michael K. Murray, Danny Stevenson, and Bai-Ling Wang. "Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories." Communications in Mathematical Physics 259, no. 3 (June 14, 2005): 577–613. http://dx.doi.org/10.1007/s00220-005-1376-8.

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36

BARAGLIA, DAVID. "CONFORMAL COURANT ALGEBROIDS AND ORIENTIFOLD T-DUALITY." International Journal of Geometric Methods in Modern Physics 10, no. 02 (December 5, 2012): 1250084. http://dx.doi.org/10.1142/s0219887812500843.

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We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified by pairs (L, H) with L a flat line bundle and H ∈ H3(M, L) a degree 3 class with coefficients in L. As a special case gerbes for the crossed module (U(1) → ℤ2) can be used to twist TM ⊕ T*M into a conformal Courant algebroid. In the exact case there is a twisted cohomology which is 4-periodic if L2 = 1. The structure of Conformal Courant algebroids on circle bundles leads us to construct a T-duality for orientifolds with free involution. This incarnation of T-duality yields an isomorphism of 4-periodic twisted cohomology. We conjecture that the isomorphism extends to an isomorphism in twisted KR-theory and give some calculations to support this claim.

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37

Bunk, Severin, and Richard J. Szabo. "Topological insulators and the Kane–Mele invariant: Obstruction and localization theory." Reviews in Mathematical Physics 32, no. 06 (December 9, 2019): 2050017. http://dx.doi.org/10.1142/s0129055x20500178.

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We present homotopy theoretic and geometric interpretations of the Kane–Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariant is related to a certain 4-equivalence which lends it an interpretation as an obstruction to a block decomposition of the sewing matrix up to non-equivariant homotopy. We prove a Mayer–Vietoris Theorem for manifolds with [Formula: see text]-actions which intertwines Real and [Formula: see text]-equivariant de Rham cohomology groups, and apply it to derive a new localization formula for the Kane–Mele invariant. This provides a unified cohomological explanation for the equivalence between the discrete Pfaffian formula and the known local geometric computations of the index for periodic lattice systems. We build on the relation between the Kane–Mele invariant and the theory of bundle gerbes with [Formula: see text]-actions to obtain geometric refinements of this obstruction and localization technique. In the preliminary part we review the Freed–Moore theory of band insulators on Galilean spacetimes with emphasis on geometric constructions, and present a bottom-up approach to time-reversal symmetric topological phases.

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38

Palmer, Sam, and Christian Sämann. "The ABJM model is a higher gauge theory." International Journal of Geometric Methods in Modern Physics 11, no. 08 (September 2014): 1450075. http://dx.doi.org/10.1142/s0219887814500753.

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Анотація:

M2-branes couple to a 3-form potential, which suggests that their description involves a non-abelian 2-gerbe or, equivalently, a principal 3-bundle. We show that current M2-brane models fit this expectation: they can be reformulated as higher gauge theories on such categorified bundles. We thus add to the still very sparse list of physically interesting higher gauge theories.

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39

Ekstrand, Christian. "k-gerbes, line bundles and anomalies." Journal of High Energy Physics 2000, no. 10 (October 23, 2000): 038. http://dx.doi.org/10.1088/1126-6708/2000/10/038.

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40

Ballico, Edoardo, and Oren Ben-Bassat. "Meromorphic Line Bundles and Holomorphic Gerbes." Mathematical Research Letters 18, no. 6 (2011): 1071–84. http://dx.doi.org/10.4310/mrl.2011.v18.n6.a3.

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41

Behrend, Kai, and Ping Xu. "S1-bundles and gerbes over differentiable stacks." Comptes Rendus Mathematique 336, no. 2 (January 2003): 163–68. http://dx.doi.org/10.1016/s1631-073x(02)00025-0.

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42

Tradler, Thomas, Scott O. Wilson, and Mahmoud Zeinalian. "Equivariant Holonomy for Bundles and Abelian Gerbes." Communications in Mathematical Physics 315, no. 1 (August 18, 2012): 39–108. http://dx.doi.org/10.1007/s00220-012-1529-5.

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43

Kragh, Thomas. "Orientations on 2-vector Bundles and Determinant Gerbes." MATHEMATICA SCANDINAVICA 113, no. 1 (September 1, 2013): 63. http://dx.doi.org/10.7146/math.scand.a-15482.

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Анотація:

In a paper from 2009, a half magnetic monopole was discovered by Ausoni, Dundas, and Rognes. This describes an obstruction to the existence of a continuous map $K(ku) \to B(ku^*)$ with determinant like properties. This magnetic monopole is in fact an obstruction to the existence of a map from $K(ku)$ to $K(\mathsf{Z},3)$, which is a retract of the natural map $K(\mathsf{Z},3) \to K(ku)$; and any sensible definition of determinant like should produce such a retract. In this paper we describe this obstruction precisely using monoidal categories. By a result from 2011 by Baas, Dundas, Richter and Rognes $K(ku)$ classifies 2-vector bundles. We thus define the notion of oriented 2-vector bundles, which removes the obstruction by the magnetic monopole. We use this to define an oriented K-theory of 2-vector bundles with a lift of the natural map from $K(\mathsf{Z},3)$. It is then possible to define a retraction of this map and since $K(\mathsf{Z},3)$ classifies complex gerbes we call this a determinant gerbe map.

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44

Murray, Michael, and Danny Stevenson. "The basic bundle gerbe on unitary groups." Journal of Geometry and Physics 58, no. 11 (November 2008): 1571–90. http://dx.doi.org/10.1016/j.geomphys.2008.07.006.

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45

Donagi, R. Y., and D. Gaitsgory Gaitsgory. "The Gerbe Of Higgs Bundles." Transformation Groups 7, no. 2 (May 1, 2002): 109–53. http://dx.doi.org/10.1007/s00031-002-0008-z.

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46

Ginot, Grégory, and Mathieu Stiénon. "$G$-gerbes, principal $2$-group bundles and characteristic classes." Journal of Symplectic Geometry 13, no. 4 (2015): 1001–47. http://dx.doi.org/10.4310/jsg.2015.v13.n4.a6.

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47

Dupont, Johan L., and Franz W. Kamber. "Gerbes, Simplicial Forms and Invariants for Families of Foliated Bundles." Communications in Mathematical Physics 253, no. 2 (October 14, 2004): 253–82. http://dx.doi.org/10.1007/s00220-004-1193-5.

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48

Park, Byungdo, and Corbett Redden. "A classification of equivariant gerbe connections." Communications in Contemporary Mathematics 21, no. 02 (February 27, 2019): 1850001. http://dx.doi.org/10.1142/s0219199718500013.

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Let [Formula: see text] be a compact Lie group acting on a smooth manifold [Formula: see text]. In this paper, we consider Meinrenken’s [Formula: see text]-equivariant bundle gerbe connections on [Formula: see text] as objects in a 2-groupoid. We prove this 2-category is equivalent to the 2-groupoid of gerbe connections on the differential quotient stack associated to [Formula: see text], and isomorphism classes of [Formula: see text]-equivariant gerbe connections are classified by degree 3 differential equivariant cohomology. Finally, we consider the existence and uniqueness of conjugation-equivariant gerbe connections on compact semisimple Lie groups.

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49

Baraglia, David. "Topological T-duality for torus bundles with monodromy." Reviews in Mathematical Physics 27, no. 03 (April 2015): 1550008. http://dx.doi.org/10.1142/s0129055x15500087.

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We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for T-duals are shown to follow. We determine necessary and sufficient conditions for existence of a T-dual in the case of affine torus bundles. This is general enough to include all principal torus bundles as well as torus bundles with arbitrary monodromy representations. We show that isomorphisms in twisted cohomology, twisted K-theory and of Courant algebroids persist in this general setting. We also give an example where twisted K-theory groups can be computed by iterating T-duality.

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50

Waldorf, Konrad. "Transgression to loop spaces and its inverse, III: Gerbes and thin fusion bundles." Advances in Mathematics 231, no. 6 (December 2012): 3445–72. http://dx.doi.org/10.1016/j.aim.2012.08.016.

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