Integral pentagon relations for 3d superconformal indices

Abstract

The superconformal index of a three-dimensional supersymmetric field theory can be expressed in terms of basic hypergeometric integrals. By comparing the indices of dual theories, one can find new integral identities for basic hypergeometric integrals. Some of these integral identities have the form of the pentagon identity which can be interpreted as the 2-3 Pachner move for triangulated 3-manifolds.

9 pages. Based on arXiv:1309.2195 with new results and comments. Presented at String-Math conference, Edmonton, Canada, June 9-13, 2014; v2: minor corrections and comments added

References in corpus (8)

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• Generalized Superconformal Index for Three Dimensional Field Theories
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Cited by in corpus (5)

• The star-triangle relation and 3d superconformal indices
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Mathematical structures behind supersymmetric dualities
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Pentagon identities arising in supersymmetric gauge theory computations