Flipping relation as a reduced star-star relation

2025/08/27 by Catak, Erdal, Mullahasanoglu, Mustafa · 2 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.19941

Abstract

In this paper, we consider the lens hyperbolic gamma solution to the star-star relation and the flipping relation from three-dimensional N=2 supersymmetric gauge theories on S³_b/ℤ_r. We explore that a certain limit of the star-star relation yields the latter symmetry transformation, which exchanges the edge interactions of two outer spins with a centrally sited spin. Furthermore, we obtain more solutions to the flipping relation in terms of the hyperbolic gamma, basic hypergeometric, and the Euler gamma functions.

Citations

• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations
• Ordinary limits of the hyperbolic hypergeometric integral identities
• Decorating the gauge/YBE correspondence
• The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I
• Comments on flavor symmetry breaking and three-dimensional superconformal index
• A remark on the q-hypergeometric integral Bailey pair and the solution to the star-triangle equation
• Lens Partition Functions and Integrability Properties
• Gamma function solutions to the star-triangle equation
• Integrability As Duality: The Gauge/YBE Correspondence
• A review on SUSY gauge theories on S³
• Hyperbolic beta integrals

Cited by

• From dual gauge theories to dual spin models
• Bailey chain approach to 2d N=(0,2) dualities

Related

• Gamma function solutions to the star-triangle equation
• The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I
• Decorating the gauge/YBE correspondence
• Lens Partition Functions and Integrability Properties
• More solutions to the decoration transformation