Integral identities for 3d dualities with SP(2N) gauge groups

Abstract

In this note we study the reduction of 4d Seiberg duality to 3d for SP(2N) SQCD with an adjoint field. We follow a general prescription that consists in compactifying the dual 4d theories on the circle. This generates an effective 3d duality. The pure 3d duality is obtained by combining the zero radius limit with a real mass flow. Here we perform this limit by a double scaling procedure: we turn on real masses proportional to the radius before shrinking the circle. We apply this mechanism to the reduction of the 4d superconformal index to the three sphere partition function. While the reduction of the 4d index on the circle is straightforward, the 3d limit necessitates the double scaling. We describe this limit on the index, finding the integral identity for the partition functions of the 3d dual theories.

25 pages, 2 figures, typos corrected

References in corpus (10)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• 3d dualities from 4d dualities
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Localization on Hopf surfaces
• Superconformal indices for N=1 theories with multiple duals
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter
• From S-confinement to 3D Chiral Theories: Dressing the Monopoles
• Transformations of elliptic hypergometric integrals
• Superconformal indices and partition functions for supersymmetric field theories

Cited by in corpus (7)

• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• String theory and the 4D/3D reduction of Seiberg duality. A Review
• Branes, partition functions and quadratic monopole superpotentials
• Lens partition function, pentagon identity and star-triangle relation
• 3d Self-Dualities
• On s-confinement in 3d $\mathcal{N}=2$ gauge theories with anti-symmetric tensors