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Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices

Spiridonov, V. P., & Vartanov, G. S. (2014). Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices. Communications in Mathematical Physics, 325(2), 421-486. doi:10.1007/s00220-013-1861-4.

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1107.5788 (Preprint), 712KB
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Creators:
Spiridonov, V. P., Author
Vartanov, G. S.1, Author
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1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Free keywords: High Energy Physics - Theory, hep-th
Abstract: We consider Seiberg electric-magnetic dualities for four-dimensional $\mathcal{N}=1$ SYM theories with $SO({N})$ gauge group. For all such theories we construct superconformal indices (SCIs) in terms of the elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to known special function identities and new highly nontrivial conjectural relations for integrals. In particular, we describe a number of new elliptic beta integrals associated with the $s$-confining theories with the spinor matter. Reductions of some dualities from $SP(2{N})$ to $SO(2{N})$ or $SO(2{N}+1)$ gauge groups are described. Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible applications of the elliptic hypergeometric integrals to a two-parameter deformation of the two-dimensional conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of the knot theory, generalized AGT duality for $(3+3)$-dimensional theories, and the 2d vortex partition function are described.

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Dates: 2011-07-282014
Publication Status: Published in print
Pages: Latex, 67 pages
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Identifiers: arXiv: 1107.5788
URI: http://arxiv.org/abs/1107.5788
DOI: 10.1007/s00220-013-1861-4
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Title: Communications in Mathematical Physics
Source Genre: Series
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Pages: - Volume / Issue: 325 (2) Sequence Number: - Start / End Page: 421 - 486 Identifier: -