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On Bailey pairs for $\mathcal N=2$ supersymmetric gauge theories on $S_b^3/\mathbb{Z}_r$

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arxiv 2210.11455 v3 pith:EI4GDYM5 submitted 2022-10-20 hep-th math-phmath.MPnlin.SI

Ilmar Gahramanov , Batuhan Keskin , Dilara Kosva , Mustafa Mullahasanoglu This is my paper · ORCID
classification hep-thmath-phmath.MPnlin.SI
keywords baileypairsgaugemathbbmathcalrelationsupersymmetrictheories
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abstract

We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional $\mathcal N=2$ supersymmetric gauge theories on $S_b^3/\mathbb{Z}_r$. The novel Bailey pairs are constructed for the star-triangle relation, the star-star relation and the pentagon identity. The first two of them are integrability conditions for the Ising-type integrable lattice models. The last one corresponds to the representation of the basic $2-3$ Pachner move for triangulated 3-manifolds.

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  1. Flipping relation as a reduced star-star relation

    hep-th 2025-08 conditional novelty 5.0 of 10

    A specific limit of the star-star relation produces the flipping relation, and new flipping solutions are given in several gamma-function families.

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