New Pentagon Identities Revisited

Abstract

We present a new solution to the pentagon identity in terms of gamma function. We obtain this solution by taking the gamma function limit from the pentagon identity related to the three-dimesional index. This limit corresponds to the identification of the sphere partition function of dual theories and being equivalent to the star-triangle relation in statistical mechanics which corresponds to the `strongly coupled' regime of the Faddeev-Volkov model.

arXiv comment4 pages, Contribution to the 32nd International Colloquium on Group Theoretical Methods in Physics, Prague, July 9-13, 2018

References in corpus (11)

• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Quantum Dilogarithm
• Abelian Current Algebra and the Virasoro Algebra on the Lattice
• Exact solution of the Faddeev-Volkov model
• The star-triangle relation and 3d superconformal indices
• A new pentagon identity for the tetrahedron index
• Basic hypergeometry of supersymmetric dualities
• Hyperbolicity of Partition Function and Quantum Gravity
• A review on SUSY gauge theories on $S^3$
• Integrable lattice spin models from supersymmetric dualities
• Pentagon identities arising in supersymmetric gauge theory computations

Cited by in corpus (2)

• Lens partition function, pentagon identity and star-triangle relation
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$