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Journal articles on the topic 'Moduli space, instanton, steiner'

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Published: 10 March 2023

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1

PARVIZI, SHAHROKH. "NONCOMMUTATIVE INSTANTONS AND THE INFORMATION METRIC." Modern Physics Letters A 17, no. 06 (February 28, 2002): 341–53. http://dx.doi.org/10.1142/s0217732302006436.

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By using the so-called Information Metric on the moduli space of an anti-self-dual (ASD) Instanton in a self-dual (SD) noncommutative background, we investigate the geometry of moduli space. The metric is evaluated perturbatively in noncommutativity parameter and we show that by putting a cutoff in the location of instanton in the definition of Information Metric we can recover the five-dimensional space–time in the presence of a B-field. This result shows that the noncommutative YM-Instanton Moduli corresponds to D-Instanton Moduli in the gravity side where the radial and transverse location of D-Instanton correspond to YM-Instanton size and location, respectively. The match is shown in the first order of noncommutativity parameter.

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2

Tian, Yu. "Conformal symmetry on the instanton moduli space." Journal of Physics A: Mathematical and General 38, no. 8 (February 10, 2005): 1823–27. http://dx.doi.org/10.1088/0305-4470/38/8/016.

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3

Ferreira, Ana Cristina. "Induced three-forms on instanton moduli spaces." International Journal of Geometric Methods in Modern Physics 11, no. 09 (October 2014): 1460041. http://dx.doi.org/10.1142/s021988781460041x.

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In this note we study a correspondence between the space of three-forms on a four-manifold and the space of three-forms on the moduli space of instantons. We then specialize to the case where the base manifold is the four-sphere.

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4

Jardim, M., and D. D. Silva. "Instanton sheaves and representations of quivers." Proceedings of the Edinburgh Mathematical Society 63, no. 4 (September 4, 2020): 984–1004. http://dx.doi.org/10.1017/s0013091520000292.

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AbstractWe study the moduli space of rank 2 instanton sheaves on ℙ3 in terms of representations of a quiver consisting of three vertices and four arrows between two pairs of vertices. Aiming at an alternative compactification for the moduli space of instanton sheaves, we show that for each rank 2 instanton sheaf, there is a stability parameter θ for which the corresponding quiver representation is θ-stable (in the sense of King), and that the space of stability parameters has a non-trivial wall-and-chamber decomposition. Looking more closely at instantons of low charge, we prove that there are stability parameters with respect to which every representation corresponding to a rank 2 instanton sheaf of charge 2 is stable and provide a complete description of the wall-and-chamber decomposition for representation corresponding to a rank 2 instanton sheaf of charge 1.

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5

BILLÓ, MARCO, PIETRO FRÈ, ALBERTO ZAFFARONI, and LUCIANO GIRARDELLO. "GRAVITATIONAL INSTANTONS IN HETEROTIC STRING THEORY: THE H-MAP AND THE MODULI DEFORMATIONS OF (4,4) SUPERCONFORMAL THEORIES." International Journal of Modern Physics A 08, no. 14 (June 10, 1993): 2351–418. http://dx.doi.org/10.1142/s0217751x9300093x.

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We study the problem of string propagation in a general instanton background for the case of the complete heterotic superstring. We define the concept of generalized hyper-Kähler manifolds and we relate it to (4,4) superconformal theories. We propose a generalized h-map construction that predicts a universal SU (6) symmetry for the modes of the string excitations moving in an instanton background. We also discuss the role of abstract N = 4 moduli and, applying it to the particular limit case of the solvable SU (2) × R instanton found by Callan et al., we show that it admits deformations and corresponds to a point in a 16-dimensional moduli space. The geometrical characterization of the other spaces in the same moduli space remains an open problem.

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6

KETOV, SERGEI V., OSVALDO P. SANTILLAN, and ANDREI G. ZORIN. "D-INSTANTON SUMS FOR MATTER HYPERMULTIPLETS." Modern Physics Letters A 19, no. 35 (November 20, 2004): 2645–53. http://dx.doi.org/10.1142/s0217732304015865.

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We calculate some nonperturbative (D-instanton) quantum corrections to the moduli space metric of several (n>1) identical matter hypermultiplets for the type-IIA superstrings compactified on a Calabi–Yau threefold, near conifold singularities. We find a nontrivial deformation of the (real) 4n-dimensional hypermultiplet moduli space metric due to the infinite number of D-instantons, under the assumption of n tri-holomorphic commuting isometries of the metric, in the hyper-Kähler limit (i.e. in the absence of gravitational corrections).

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7

Jardim, Marcos, and Misha Verbitsky. "Trihyperkähler reduction and instanton bundles on." Compositio Mathematica 150, no. 11 (August 27, 2014): 1836–68. http://dx.doi.org/10.1112/s0010437x14007477.

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AbstractA trisymplectic structure on a complex $2n$-manifold is a three-dimensional space ${\rm\Omega}$ of closed holomorphic forms such that any element of ${\rm\Omega}$ has constant rank $2n$, $n$ or zero, and degenerate forms in ${\rm\Omega}$ belong to a non-degenerate quadric hypersurface. We show that a trisymplectic manifold is equipped with a holomorphic 3-web and the Chern connection of this 3-web is holomorphic, torsion-free, and preserves the three symplectic forms. We construct a trisymplectic structure on the moduli of regular rational curves in the twistor space of a hyperkähler manifold, and define a trisymplectic reduction of a trisymplectic manifold, which is a complexified form of a hyperkähler reduction. We prove that the trisymplectic reduction in the space of regular rational curves on the twistor space of a hyperkähler manifold $M$ is compatible with the hyperkähler reduction on $M$. As an application of these geometric ideas, we consider the ADHM construction of instantons and show that the moduli space of rank $r$, charge $c$ framed instanton bundles on $\mathbb{C}\mathbb{P}^{3}$ is a smooth trisymplectic manifold of complex dimension $4rc$. In particular, it follows that the moduli space of rank two, charge $c$ instanton bundles on $\mathbb{C}\mathbb{P}^{3}$ is a smooth complex manifold dimension $8c-3$, thus settling part of a 30-year-old conjecture.

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8

Teleman, Andrei. "Analytic cycles in flip passages and in instanton moduli spaces over non-Kählerian surfaces." International Journal of Mathematics 27, no. 07 (June 2016): 1640009. http://dx.doi.org/10.1142/s0129167x16400097.

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Let [Formula: see text] ([Formula: see text]) be a moduli space of stable (polystable) bundles with fixed determinant on a complex surface with [Formula: see text] and let [Formula: see text] be a pure [Formula: see text]-dimensional analytic set. We prove a general formula for the homological boundary [Formula: see text] of the Borel–Moore fundamental class of [Formula: see text] in the boundary of the blown up moduli space [Formula: see text]. The proof is based on the holomorphic model theorem of [A. Teleman, Instanton moduli spaces on non-Kählerian surfaces, Holomorphic models around the reduction loci, J. Geom. Phys. 91 (2015) 66–87] which identifies a neighborhood of a boundary component of [Formula: see text] with a neighborhood of the boundary of a “blown up flip passage”. We then focus on a particular instanton moduli space which intervenes in our program for proving the existence of curves on class VII surfaces. Using our result, combined with general properties of the Donaldson cohomology classes, we prove incidence relations between the Zariski closures (in the considered moduli space) of certain families of extensions. These incidence relations are crucial for understanding the geometry of the moduli space, and cannot be obtained using classical complex geometric deformation theory.

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9

Bischoff, Jan, and Olaf Lechtenfeld. "Path-Integral Quantization of the (2,2) String." International Journal of Modern Physics A 12, no. 27 (October 30, 1997): 4933–71. http://dx.doi.org/10.1142/s0217751x97002632.

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A complete treatment of the (2,2) NSR string in flat (2 + 2)-dimensional space–time is given, from the formal path integral over N = 2 super Riemann surfaces to the computational recipe for amplitudes at any loop or gauge instanton number. We perform in detail the superconformal gauge fixing, discuss the spectral flow, and analyze the supermoduli space with emphasis on the gauge moduli. Background gauge field configurations in all instanton sectors are constructed. We develop chiral bosonization on punctured higher-genus surfaces in the presence of gauge moduli and instantons. The BRST cohomology is recapitulated, with a new space–time interpretation for picture-changing. We point out two ways of combining left- and right-movers, which lead to different three-point functions.

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10

Casnati, Gianfranco, and Ozhan Genc. "Instanton bundles on two Fano threefolds of index 1." Forum Mathematicum 32, no. 5 (September 1, 2020): 1315–36. http://dx.doi.org/10.1515/forum-2019-0189.

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AbstractWe deal with instanton bundles on the product {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.

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11

Awata, Hidetoshi, and Hiroaki Kanno. "Instanton counting, Macdonald function and the moduli space ofD-branes." Journal of High Energy Physics 2005, no. 05 (May 17, 2005): 039. http://dx.doi.org/10.1088/1126-6708/2005/05/039.

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12

Katsylo, Pavel I., and Giorgio Ottaviani. "Regularity of the moduli space of instanton bundles MIP3(5)." Transformation Groups 8, no. 2 (June 2003): 147–58. http://dx.doi.org/10.1007/s00031-003-0109-3.

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13

Sako, A., and T. Sasaki. "Euler number of instanton moduli space and Seiberg–Witten invariants." Journal of Mathematical Physics 42, no. 1 (January 2001): 130–57. http://dx.doi.org/10.1063/1.1331319.

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14

CARTAS-FUENTEVILLA, R., A. ESCALANTE-HERNANDEZ, and J. BERRA-MONTIEL. "DIMENSION OF THE MODULI SPACE AND HAMILTONIAN ANALYSIS OF BF FIELD THEORIES." International Journal of Modern Physics A 26, no. 18 (July 20, 2011): 3013–34. http://dx.doi.org/10.1142/s0217751x11053717.

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By using the Atiyah–Singer theorem through some similarities with the instanton and the antiinstanton moduli spaces, the dimension of the moduli space for two- and four-dimensional BF theories valued in different background manifolds and gauge groups scenarios is determined. Additionally, we develop Dirac's canonical analysis for a four-dimensional modified BF theory, which reproduces the topological YM theory. This framework will allow us to understand the local symmetries, the constraints, the extended Hamiltonian and the extended action of the theory.

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15

FLUME, R., H. STORCH, and R. POGHOSSIAN. "THE SEIBERG–WITTEN PREPOTENTIAL AND THE EULER CLASS OF THE REDUCED MODULI SPACE OF INSTANTONS." Modern Physics Letters A 17, no. 06 (February 28, 2002): 327–39. http://dx.doi.org/10.1142/s0217732302006588.

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The n-instanton contribution to the Seiberg–Witten prepotential of N = 2 supersymmetric d = 4 Yang–Mills theory is represented as the integral of the exponential of an equivariantly exact form. Integrating out an overall scale and a U(1) angle the integral is rewritten as (4n - 3)-fold product of a closed two-form. This two-form is, formally, a representative of the Euler class of the instanton moduli space viewed as a principal U(1) bundle, because its pullback under bundle projection is the exterior derivative of an angular one-form.

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16

Jardim, Marcos, Mario Maican, and Alexander Tikhomirov. "Moduli spaces of rank 2 instanton sheaves on the projective space." Pacific Journal of Mathematics 291, no. 2 (September 14, 2017): 399–424. http://dx.doi.org/10.2140/pjm.2017.291.399.

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17

Dabrowski, Ludwik, Thomas Krajewski, and Giovanni Landi. "Non-linear σ-models in noncommutative geometry: fields with values in finite spaces." Modern Physics Letters A 18, no. 33n35 (November 20, 2003): 2371–79. http://dx.doi.org/10.1142/s0217732303012593.

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We study σ-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space [Formula: see text].

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18

HENNI, ABDELMOUBINE AMAR, MARCOS JARDIM, and RENATO VIDAL MARTINS. "ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES." Glasgow Mathematical Journal 57, no. 2 (December 18, 2014): 285–321. http://dx.doi.org/10.1017/s0017089514000305.

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AbstractWe present a construction of framed torsion free instanton sheaves on a projective variety containing a fixed line which further generalises the one on projective spaces. This is done by generalising the so called ADHM variety. We show that the moduli space of such objects is a quasi projective variety, which is fine in the case of projective spaces. We also give an ADHM categorical description of perverse instanton sheaves in the general case, along with a hypercohomological characterisation of these sheaves in the particular case of projective spaces.

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19

BELHAJ, A., and E. H. SAIDI. "ON HYPER-KAHLER SINGULARITIES." Modern Physics Letters A 15, no. 29 (September 21, 2000): 1767–79. http://dx.doi.org/10.1142/s0217732300001638.

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Using a geometric realization of the SU (2)R symmetry and a procedure of factorization of the gauge and SU (2)R charges, we study the small instanton singularities of the Higgs branch of supersymmetric U (1)r gauge theories with eight supercharges. We derive new solutions for the moduli space of vacua preserving manifestly the eight supercharges. In particular, we obtain an extension of the ordinary ADE singularities for hyper-Kahler manifolds and show that the classical moduli space of vacua is in general given by cotangent bundles of compact weighted projective spaces.

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20

CURIO, GOTTFRIED. "SUPERPOTENTIAL OF THE M-THEORY CONIFOLD AND TYPE IIA STRING THEORY." International Journal of Modern Physics A 19, no. 04 (February 10, 2004): 521–55. http://dx.doi.org/10.1142/s0217751x04017720.

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The membrane instanton superpotential for M-theory on the G2 holonomy manifold given by the cone on S3×S3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.

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21

Tikhomirov, Aleksandr S. "Moduli of mathematical instanton vector bundles with odd $ c_2$ on projective space." Izvestiya: Mathematics 76, no. 5 (October 26, 2012): 991–1073. http://dx.doi.org/10.1070/im2012v076n05abeh002613.

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22

Tikhomirov, A. S. "Moduli of mathematical instanton vector bundles with even $ c_2$ on projective space." Izvestiya: Mathematics 77, no. 6 (December 23, 2013): 1195–223. http://dx.doi.org/10.1070/im2013v077n06abeh002674.

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23

Choy, Jaeyoo. "The SO(3)-instanton moduli space and tensor products of ADHM data." Journal of Algebra 528 (June 2019): 38–71. http://dx.doi.org/10.1016/j.jalgebra.2019.03.004.

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24

Etesi, Gábor, and Szilárd Szabó. "Harmonic Functions and Instanton Moduli Spaces on the Multi-Taub–NUT Space." Communications in Mathematical Physics 301, no. 1 (October 6, 2010): 175–214. http://dx.doi.org/10.1007/s00220-010-1146-0.

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25

Matone, Marco. "The instanton universal moduli space of N=2 supersymmetric Yang–Mills theory." Physics Letters B 514, no. 1-2 (August 2001): 161–64. http://dx.doi.org/10.1016/s0370-2693(01)00783-3.

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26

KOBAYASHI, TATSUO, and NORIYASU OHTSUBO. "GEOMETRICAL ASPECTS OF ZN ORBIFOLD PHENOMENOLOGY." International Journal of Modern Physics A 09, no. 01 (January 10, 1994): 87–125. http://dx.doi.org/10.1142/s0217751x94000054.

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We study the geometrical and phenomenological aspects of ZN orbifold models. Conditions on the background moduli and Wilson lines are clarified. We investigate the explicit ZN-invariant states through a modified GSO projection and calculate Yukawa coupling conditions due to space-group and SO(10) invariance. We estimate a contribution of a holomorphic instanton to the couplings.

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27

Bruzzo, Ugo, Dimitri Markushevich, and Alexander S. Tikhomirov. "Moduli of symplectic instanton vector bundles of higher rank on projective space ℙ3." Central European Journal of Mathematics 10, no. 4 (April 28, 2012): 1232–45. http://dx.doi.org/10.2478/s11533-012-0062-2.

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28

Kamiyama, Yasuhiko, Akira Kono, and Michishige Tezuka. "Cohomology of the moduli space of SO(n)-instantons with instanton number 1." Topology and its Applications 146-147 (January 2005): 471–87. http://dx.doi.org/10.1016/j.topol.2003.08.031.

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29

Andrade, Aline V., Simone Marchesi, and Rosa M. Miró-Roig. "Irreducibility of the moduli space of orthogonal instanton bundles on $$\mathbb {P}^n$$." Revista Matemática Complutense 33, no. 1 (July 29, 2019): 271–94. http://dx.doi.org/10.1007/s13163-019-00317-y.

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30

Ivanova, Tatiana A. "Scattering of instantons, monopoles and vortices in higher dimensions." International Journal of Geometric Methods in Modern Physics 13, no. 03 (March 2016): 1650032. http://dx.doi.org/10.1142/s0219887816500328.

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In this paper, we consider Yang–Mills theory on manifolds [Formula: see text] with a [Formula: see text]-dimensional Riemannian manifold [Formula: see text] of special holonomy admitting gauge instanton equations. Instantons are considered as particle-like solutions in [Formula: see text] dimensions whose static configurations are concentrated on [Formula: see text]. We study how they evolve in time when considered as solutions of the Yang–Mills equations on [Formula: see text] with moduli depending on time [Formula: see text]. It is shown that in the adiabatic limit, when the metric in the [Formula: see text] direction is scaled down, the classical dynamics of slowly moving instantons corresponds to a geodesic motion in the moduli space [Formula: see text] of gauge instantons on [Formula: see text]. Similar results about geodesic motion in the moduli space of monopoles and vortices in higher dimensions are briefly discussed.

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31

GRANT, JONATHAN. "THE MODULI PROBLEM OF LOBB AND ZENTNER AND THE COLORED 𝔰𝔩(N) GRAPH INVARIANT." Journal of Knot Theory and Its Ramifications 22, no. 10 (September 2013): 1350060. http://dx.doi.org/10.1142/s0218216513500600.

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Motivated by a possible connection between the SU (N) instanton knot Floer homology of Kronheimer and Mrowka and 𝔰𝔩(N) Khovanov–Rozansky homology, Lobb and Zentner recently introduced a moduli problem associated to colorings of trivalent graphs of the kind considered by Murakami, Ohtsuki and Yamada in their state-sum interpretation of the quantum 𝔰𝔩(N) knot polynomial. For graphs with two colors, they showed this moduli space can be thought of as a representation variety, and that its Euler characteristic is equal to the 𝔰𝔩(N) polynomial of the graph evaluated at 1. We extend their results to graphs with arbitrary colorings by irreducible anti-symmetric representations of 𝔰𝔩(N).

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32

Kamiyama, Yasuhiko. "Some Remarks on the Homology of Moduli Space of Instantons with Instanton Number 2." Proceedings of the American Mathematical Society 112, no. 1 (May 1991): 297. http://dx.doi.org/10.2307/2048510.

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33

Kamiyama, Yasuhiko. "Some remarks on the homology of moduli space of instantons with instanton number $2$." Proceedings of the American Mathematical Society 112, no. 1 (January 1, 1991): 297. http://dx.doi.org/10.1090/s0002-9939-1991-1045595-7.

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34

Tikhomirov, A. A. "The main component of the moduli space of mathematical instanton vector bundles on P3." Journal of Mathematical Sciences 86, no. 5 (October 1997): 3004–87. http://dx.doi.org/10.1007/bf02355113.

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35

Papoulias, Vasileios Ektor. "Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric." Communications in Mathematical Physics 384, no. 3 (May 17, 2021): 2009–66. http://dx.doi.org/10.1007/s00220-021-04055-5.

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AbstractWe use the highly symmetric Stenzel Calabi–Yau structure on $$T^{\star }S^{4}$$ T ⋆ S 4 as a testing ground for the relationship between the Spin(7) instanton and Hermitian–Yang–Mills (HYM) equations. We reduce both problems to tractable ODEs and look for invariant solutions. In the abelian case, we establish local equivalence and prove a global nonexistence result. We analyze the nonabelian equations with structure group SO(3) and construct the moduli space of invariant Spin(7) instantons in this setting. This is comprised of two 1-parameter families—one of them explicit—of irreducible Spin(7) instantons. Each carries a unique HYM connection. We thus negatively resolve the question regarding the equivalence of the two gauge theoretic PDEs. The HYM connections play a role in the compactification of this moduli space, exhibiting a removable singularity phenomenon that we aim to further examine in future work.

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36

Habermann, Lutz. "TheL 2-metric on the moduli space ofSU(2)-instantons with instanton number 1 over the Euclidean 4-space." Annals of Global Analysis and Geometry 11, no. 4 (November 1993): 311–22. http://dx.doi.org/10.1007/bf00773547.

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37

Antoniadis, I., and B. Pioline. "Higgs Branch, Hyper-Kähler Quotient and Duality in SUSY N = 2 Yang–Mills Theories." International Journal of Modern Physics A 12, no. 27 (October 30, 1997): 4907–31. http://dx.doi.org/10.1142/s0217751x97002620.

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Low-energy limits of N = 2 supersymmetric field theories in the Higgs branch are described in terms of a nonlinear four-dimensional σ-model on a hyper-Kähler target space, classically obtained as a hyper-Kähler quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low-energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg–Witten SU(2) theory with Nf flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on ℝ4. By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a U(1) N = 2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg–Witten's theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of U(Nc)Nf flavors and U(Nf-Nc)Nf flavors theories, by using a geometric interpretation due to Biquard et al. This duality may be relevant for understanding Seiberg's conjectured duality Nc ↔ Nf-Nc in N = 1 SUSY SU(Nc) gauge theories.

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38

BAUTISTA, R., J. MUCIÑO, E. NAHMAD-ACHAR, and M. ROSENBAUM. "CLASSIFICATION OF GAUGE-RELATED INVARIANT CONNECTIONS." Reviews in Mathematical Physics 05, no. 01 (March 1993): 69–103. http://dx.doi.org/10.1142/s0129055x93000036.

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Connection 1-forms on principal fiber bundles with arbitrary structure groups are considered, and a characterization of gauge-equivalent connections in terms of their associated holonomy groups is given. These results are then applied to invariant connections in the case where the symmetry group acts transitively on fibers, and both local and global conditions are derived which lead to an algebraic procedure for classifying orbits in the moduli space of these connections. As an application of the developed techniques, explicit solutions for SU (2) × SU (2)-symmetric connections over S2 × S2, with SU(2) structure group, are derived and classified into non-gauge-related families, and multi-instanton solutions are identified.

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39

Dasgupta, Keshav, and Jihye Seo. "A note on the stringy embeddings of certain N=2 dualities." Canadian Journal of Physics 91, no. 6 (June 2013): 463–64. http://dx.doi.org/10.1139/cjp-2013-0126.

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Seiberg–Witten theory can be embedded in F-theory using D3 branes probing an orientifold geometry. The nonperturbative corrections in the orientifold picture map directly to the instanton corrections in the corresponding gauge theory that convert the classical moduli space to the quantum one. In this short review we argue that the recently proposed class of conformal Gaiotto models may also be embedded in F-theory. The F-theory constructions help us not only to understand the Gaiotto dualities but also to extend to the nonconformal cases with and without cascading behaviors. For the conformal cases, the near horizon geometries in F-theory capture both the UV and IR behaviors succinctly.

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40

Billo, Marco, Marialuisa Frau, Igor Pesando, and Alberto Lerda. "N=1/2 gauge theory and its instanton moduli space from open strings in R-R background." Journal of High Energy Physics 2004, no. 05 (May 11, 2004): 023. http://dx.doi.org/10.1088/1126-6708/2004/05/023.

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41

OH, YONG-GEUN, and RUI WANG. "ANALYSIS OF CONTACT CAUCHY–RIEMANN MAPS II: CANONICAL NEIGHBORHOODS AND EXPONENTIAL CONVERGENCE FOR THE MORSE–BOTT CASE." Nagoya Mathematical Journal 231 (May 15, 2017): 128–223. http://dx.doi.org/10.1017/nmj.2017.17.

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This is a sequel to the papers Oh and Wang (Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics 106 (2014), 43–63, eds. by Y.-J. Suh and et al. for ICM-2014 satellite conference, Daejeon, Korea, August 2014; arXiv:1212.4817; Analysis of contact Cauchy–Riemann maps I: a priori$C^{k}$estimates and asymptotic convergence, submitted, preprint, 2012, arXiv:1212.5186v3). In Oh and Wang (Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics 106 (2014), 43–63, eds. by Y.-J. Suh and et al. for ICM-2014 satellite conference, Daejeon, Korea, August 2014; arXiv:1212.4817), the authors introduced a canonical affine connection on $M$ associated to the contact triad $(M,\unicode[STIX]{x1D706},J)$. In Oh and Wang (Analysis of contact Cauchy–Riemann maps I: a priori$C^{k}$estimates and asymptotic convergence, submitted, preprint, 2012, arXiv:1212.5186v3), they used the connection to establish a priori$W^{k,p}$-coercive estimates for maps $w:\dot{\unicode[STIX]{x1D6F4}}\rightarrow M$ satisfying $\overline{\unicode[STIX]{x2202}}^{\unicode[STIX]{x1D70B}}w=0$, $d(w^{\ast }\unicode[STIX]{x1D706}\circ j)=0$without involving symplectization. We call such a pair $(w,j)$ a contact instanton. In this paper, we first prove a canonical neighborhood theorem of the locus $Q$ foliated by closed Reeb orbits of a Morse–Bott contact form. Then using a general framework of the three-interval method, we establish exponential decay estimates for contact instantons $(w,j)$ of the triad $(M,\unicode[STIX]{x1D706},J)$, with $\unicode[STIX]{x1D706}$ a Morse–Bott contact form and $J$ a CR-almost complex structure adapted to $Q$, under the condition that the asymptotic charge of $(w,j)$ at the associated puncture vanishes.We also apply the three-interval method to the symplectization case and provide an alternative approach via tensorial calculations to exponential decay estimates in the Morse–Bott case for the pseudoholomorphic curves on the symplectization of contact manifolds. This was previously established by Bourgeois (A Morse–Bott approach to contact homology, Ph.D. dissertation, Stanford University, 2002) (resp. by Bao (On J-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends, Pacific J. Math. 278(2) (2015), 291–324)), by using special coordinates, for the cylindrical (resp. for the asymptotically cylindrical) ends. The exponential decay result for the Morse–Bott case is an essential ingredient in the setup of the moduli space of pseudoholomorphic curves which plays a central role in contact homology and symplectic field theory (SFT).

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42

Benvenuti, Sergio, Amihay Hanany, and Noppadol Mekareeya. "The Hilbert series of the one instanton moduli space." Journal of High Energy Physics 2010, no. 6 (June 2010). http://dx.doi.org/10.1007/jhep06(2010)100.

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43

Pomoni, Elli, Wenbin Yan, and Xinyu Zhang. "Tetrahedron Instantons." Communications in Mathematical Physics, April 20, 2022. http://dx.doi.org/10.1007/s00220-022-04376-z.

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AbstractWe introduce and study tetrahedron instantons, which can be realized in string theory by $$\hbox {D}1$$ D 1 -branes probing a configuration of intersecting $$\hbox {D}7$$ D 7 -branes in flat spacetime with a proper constant B-field. Physically they capture instantons on $$\mathbb {C}^{3}$$ C 3 in the presence of the most general intersecting real codimension-two supersymmetric defects. Moreover, we construct the tetrahedron instantons as particular solutions of general instanton equations in noncommutative field theory. We analyze the moduli space of tetrahedron instantons and discuss the geometric interpretations. We compute the instanton partition function both via the equivariant localization on the moduli space of tetrahedron instantons and via the elliptic genus of the worldvolume theory on the $$\hbox {D}1$$ D 1 -branes probing the intersecting $$\hbox {D}7$$ D 7 -branes, obtaining the same result. The instanton partition function of the tetrahedron instantons lies between the higher-rank Donaldson–Thomas invariants on $$\mathbb {C}^{3}$$ C 3 and the partition function of the magnificent four model, which is conjectured to be the mother of all instanton partition functions. Finally, we show that the instanton partition function admits a free field representation, suggesting the existence of a novel kind of symmetry which acts on the cohomology of the moduli spaces of tetrahedron instantons.

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Halcrow, Chris, and Thomas Winyard. "A consistent two-skyrmion configuration space from instantons." Journal of High Energy Physics 2021, no. 12 (December 2021). http://dx.doi.org/10.1007/jhep12(2021)039.

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Abstract To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a vector meson which we identify with the ρ-meson. Each instanton generates a unique skyrmion and we reinterpret the 8N instanton moduli as physical degrees of freedom in the Skyrme model. In this picture a single skyrmion has six zero modes and two non-zero modes: one controls the overall scale of the solution and one the energy of the ρ-meson field. We study the N = 1 and N = 2 systems in detail. Two interacting skyrmions can excite the ρ through scattering, suggesting that the ρ and Skyrme fields are intrinsically linked. Our proposal is the first consistent manifold description of the two-skyrmion configuration space. The method can also be generalised to higher N and thus provides a general framework to study any skyrmion configuration space.

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Jardim, Marcos, Dimitri Markushevich, and Alexander S. Tikhomirov. "New Divisors in the Boundary of the Instanton Moduli Space." Moscow Mathematical Journal 18, no. 1 (2018). http://dx.doi.org/10.17323/1609-4514-2018-18-1-117-148.

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46

Billò, M., M. Frau, F. Fucito, L. Gallot, A. Lerda, and J. F. Morales. "On the D(–1)/D7-brane systems." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)096.

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Abstract We study non-perturbative effects in supersymmetric U(N) gauge theories in eight dimensions realized by means of D(–1)/D7-brane systems with non-trivial world-volume fluxes turned on. Using an explicit string construction in terms of vertex operators, we derive the action for the open strings ending on the D(–1)-branes and exhibit its BRST structure. The space of vacua for these open strings is shown to be in correspondence with the moduli space of generalized ADHM gauge connections which trigger the non-perturbative corrections in the eight-dimensional theory. These corrections are computed via localization and turn out to depend on the curved background used to localize the integrals on the instanton moduli space, and vanish in flat space. Finally, we show that for specific choices of the background the instanton partition functions reduce to weighted sums of the solid partitions of the integers.

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47

Cecotti, Sergio. "Moduli spaces of Calabi-Yau d-folds as gravitational-chiral instantons." Journal of High Energy Physics 2020, no. 12 (December 2020). http://dx.doi.org/10.1007/jhep12(2020)008.

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Abstract Motivated by the swampland program, we show that the Weil-Petersson geometry of the moduli space of a Calabi-Yau manifold of complex dimension d ≤ 4 is a gravitational instanton (i.e. a finite-action solution of the Euclidean equations of motion of gravity with matter). More precisely, the moduli geometry of Calabi-Yau d-folds (d ≤ 4) describes instantons of (E)AdS Einstein gravity coupled to a standard chiral model.From the point of view of the low-energy physics of string/M-theory compactified on the Calabi-Yau X, the various fields propagating on its moduli space are the couplings appearing in the effective Lagrangian "Image missing".

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48

Sen, Ashoke. "D-instanton perturbation theory." Journal of High Energy Physics 2020, no. 8 (August 2020). http://dx.doi.org/10.1007/jhep08(2020)075.

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Abstract D-instanton world-volume theory has open string zero modes describing collective coordinates of the instanton. The usual perturbative amplitudes in the D-instanton background suffer from infra-red divergences due to the presence of these zero modes, and the usual approach of analytic continuation in momenta does not work since all open string states on a D-instanton carry strictly zero momentum. String field theory is well-suited for tackling these issues. However we find a new subtlety due to the existence of additional zero modes in the ghost sector. This causes a breakdown of the Siegel gauge, but a different gauge fixing consistent with the BV formalism renders the perturbation theory finite and unambiguous. At each order, this produces extra contribution to the amplitude besides what is obtained from integration over the moduli space of Riemann surfaces.

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Kimura, Takuya, Takahiro Nishinaka, Yuji Sugawara, and Takahiro Uetoko. "Argyres-Douglas theories, S-duality and AGT correspondence." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)205.

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Abstract We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional $$ \mathcal{N} $$ N = 2 U(2) gauge theories coupled to (A1, D2n) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to the case of U(2) gauge group, which requires us to define irregular states of the direct sum of Virasoro and Heisenberg algebras. Using our formula, one can evaluate the contribution of the (A1, D2n) theory at each fixed point on the U(2) instanton moduli space. As an application, we evaluate the instanton partition function of the (A3, A3) theory to find it in a peculiar relation to that of SU(2) gauge theory with four fundamental flavors. From this relation, we read off how the S-duality group acts on the UV gauge coupling of the (A3, A3) theory.

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Cortés, Vicente, and Iván Tulli. "Quaternionic Kähler Metrics Associated to Special Kähler Manifolds with Mutually Local Variations of BPS Structures." Annales Henri Poincaré, January 5, 2022. http://dx.doi.org/10.1007/s00023-021-01145-x.

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AbstractWe construct a quaternionic Kähler manifold from a conical special Kähler manifold with a certain type of mutually local variation of BPS structures. We give global and local explicit formulas for the quaternionic Kähler metric and specify under which conditions it is positive-definite. Locally, the metric is a deformation of the 1-loop corrected Ferrara–Sabharwal metric obtained via the supergravity c-map. The type of quaternionic Kähler metrics we obtain is related to work in the physics literature by S. Alexandrov and S. Banerjee, where they discuss the hypermultiplet moduli space metric of type IIA string theory, with mutually local D-instanton corrections.

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