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arXiv · 2210.11455

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

Ilmar Gahramanov·Batuhan Keskin·Dilara Kosva·Mustafa Mullahasanoglu
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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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Ilmar Gahramanov, Batuhan Keskin, Dilara Kosva, Mustafa Mullahasanoglu. 2022-10-20. On Bailey pairs for $\mathcal N=2$ supersymmetric gauge theories on $S_b^3/\mathbb{Z}_r$. https://doi.org/10.1007/jhep03(2023)169

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