Lens partition function, pentagon identity, and star-triangle relation

Lens Partition Functions and Integrability Properties

“…In this section, we explain the work [36] and give some details of the new result by applying gauge symmetry breaking. The idea is first done in [8] (see also [37]) for the duality of partition functions on S 3 b and used in [4] for the dual theories on S 3 b /Z r so for details both studies represent the way of doing gauge symmetry breaking step by step.…”

“…In the schematic diagram, gauge groups such as SU (2) or U (1) × U (1) will be represented on the vertices. Bifundamental matter sits on the edges and the arrow will play a role to specify fundamental (outgoing arrow) and antifundamental (incoming arrow) representations 4 as rapidity lines to specify horizontal and vertical interaction types (explained in Sec.2 in details) 5 . Supersymmetric quiver gauge theory shares the partition function with the corresponding integrable spin lattice model.…”

“…Factorization is the division of the four spin interactions into four interactions of two spins. YBE| Star-triangle relation [4] SU SY | G : U (1) F : SU (4) × SU (4) YBE| Star-star relation [5] derivation derivation gauge symmetry breaking gauge symmetry breaking In the present study, we complete the scheme.…”

“…[6,7]. The correspondence enables us to write the star-triangle relation [3,4,[8][9][10] or the star-star relations [5,11,12] of exactly solvable lattice spin models in statistical mechanics with the interpretation of integral identities resulting from the equality of supersymmetric partition functions. Simply, the duality of two supersymmetric gauge theories gives us an integral identity and this identity can be interpreted as the star-triangle relation or the star-star relation.…”

Bailey pairs for the q-hypergeometric integral pentagon identity

“…Such identities also play a role in the study of supersymmetric gauge theories, integrable models, knot theory, etc. (see some recent works [3][4][5][6][7][8][9][10][11]).…”