Lens partition function, pentagon identity, and startriangle relation
Abstract
We study the threedimensional lens partition function for N =2 supersymmetric gauge dual theories on S^{3}/Z_{r} by using the gauge/YangBaxter equation correspondence. This correspondence relates supersymmetric gauge theories to exactly solvable models of statistical mechanics. The equality of partition functions for the threedimensional supersymmetric dual theories can be written as an integral identity for hyperbolic hypergeometric functions. We obtain such an integral identity which can be written as the startriangle relation for Ising type integrable models and as the integral pentagon identity. The latter represents the basic 23 Pachner move for triangulated 3manifolds. A special case of our integral identity can be used for proving orthogonality and completeness relation of the ClebschGordan coefficients for the selfdual continuous series of U_{q}(o s p (1 2 )).
 Publication:

Physical Review D
 Pub Date:
 June 2021
 DOI:
 10.1103/PhysRevD.103.126013
 arXiv:
 arXiv:2009.14198
 Bibcode:
 2021PhRvD.103l6013B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 16T25;
 33Cxx;
 33Dxx
 EPrint:
 22 pages, v2: minor corrections and comments, v3: minor corrections