Mathematical structures behind supersymmetric dualities

Abstract

The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.

10 pages, v2: minor corrections, comments and refs. added

References in corpus (14)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• Generalized Superconformal Index for Three Dimensional Field Theories
• Essays on the theory of elliptic hypergeometric functions
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Superconformal indices for N=1 theories with multiple duals
• Calculating the Superconformal Index and Seiberg Duality
• The star-triangle relation and 3d superconformal indices
• Supersymmetric dualities beyond the conformal window
• Transformations of elliptic hypergometric integrals
• Basic hypergeometry of supersymmetric dualities
• Integral pentagon relations for 3d superconformal indices
• Multiple sine, multiple elliptic gamma functions and rational cones
• A journey to 3d: exact relations for adjoint SQCD from dimensional reduction

Cited by in corpus (6)

• Basic hypergeometry of supersymmetric dualities
• Integrable lattice spin models from supersymmetric dualities
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• Pentagon identities arising in supersymmetric gauge theory computations
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$