Basic hypergeometry of supersymmetric dualities

Abstract

We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic proofs and physical interpretations of the presented identities.

25 pages, v2: minor corrections and comments

References in corpus (11)

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Cited by in corpus (10)

• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Integrable lattice spin models from supersymmetric dualities
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Lens partition function, pentagon identity and star-triangle relation
• Pentagon identities arising in supersymmetric gauge theory computations
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• New Pentagon Identities Revisited
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations