A new pentagon identity for the tetrahedron index

Abstract

Recently Kashaev, Luo and Vartanov, using the reduction from a four-dimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following their idea we have obtained a new pentagon identity for a certain combination of so-called tetrahedron indices arising from the equality of superconformal indices of dual three-dimensional N=2 supersymmetric theories and give a mathematical proof of it.

13 pages, v2: we added a new section with the proof of the identity, misprints corrected

References in corpus (12)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• 3d dualities from 4d dualities
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons 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
• Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group
• On the ISS model of dynamical SUSY breaking
• Supersymmetric dualities beyond the conformal window
• Superconformal indices and partition functions for supersymmetric field theories
• Aspects of elliptic hypergeometric functions

Cited by in corpus (16)

• 3d N=2 mirror symmetry, pq-webs and monopole superpotentials
• New solutions of the star-triangle relation with discrete and continuous spin variables
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• The star-triangle relation and 3d superconformal indices
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• Basic hypergeometry of supersymmetric dualities
• Integrable lattice spin models from supersymmetric dualities
• Mathematical structures behind supersymmetric dualities
• Integral pentagon relations for 3d superconformal indices
• Lens partition function, pentagon identity and star-triangle relation
• 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
• New Pentagon Identities Revisited
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$