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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.
