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Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices

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Abstract

We consider Seiberg electric-magnetic dualities for 4d \({\mathcal{N} = 1}\) SYM theories with SO(N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to proven earlier special function identities and new 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 fields. Reductions of some dualities from SP(2N) to SO(2N) or SO(2N + 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 2d conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of knot theory, generalized AGT duality for (3 + 3)d theories, and a 2d vortex partition function are described.

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  1. G. S. Vartanov

    Present address: DESY Theory, Notkestr. 85, 22603, Hamburg, Germany

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow Region, 141980, Russia

    V. P. Spiridonov

  2. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476, Golm, Germany

    G. S. Vartanov

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  1. V. P. Spiridonov
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Communicated by N. A. Nekrasov

Dedicated to D.I. Kazakov on the occasion of his 60th birthday

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Spiridonov, V.P., Vartanov, G.S. Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices. Commun. Math. Phys. 325, 421–486 (2014). https://doi.org/10.1007/s00220-013-1861-4

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