# New Pentagon Identities Revisited

@article{Jafarzade2018NewPI, title={New Pentagon Identities Revisited}, author={Shahriyar Jafarzade}, journal={Journal of Physics: Conference Series}, year={2018}, volume={1194} }

We present a new solution to the pentagon identity in terms of gamma function. We obtain this solution by taking the gamma function limit from the pentagon identity related to the three-dimesional index. This limit corresponds to the identification of the sphere partition function of dual theories and being equivalent to the star-triangle relation in statistical mechanics which corresponds to the “strongly coupled” regime of the Faddeev-Volkov model.

## 6 Citations

### Bailey pairs for the q-hypergeometric integral pentagon identity

- Mathematics
- 2021

In this work, we construct new Bailey pairs for the integral pentagon identity in terms of qhypergeometric functions. The pentagon identity considered here represents equality of the partition…

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

- MathematicsPhysical Review D
- 2021

We study the three-dimensional lens partition function for $\mathcal N=2$ supersymmetric gauge dual theories on $S^3/\mathbb{Z}_r$ by using the gauge/YBE correspondence. This correspondence relates…

### Lens Partition Functions and Integrability Properties

- Physics, Mathematics
- 2021

: We study lens partitions functions for the three-dimensional N = 2 supersymmetric gauge theories on S 3 b / Z r . We consider an equality as a new hyperbolic hypergeometric solution to the…

### D ec 2 02 2 On Bailey pairs for N = 2 supersymmetric gauge theories on S 3 b / Z r

- Mathematics
- 2022

We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional N = 2 supersymmetric gauge…

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

- Mathematics
- 2022

: We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional N = 2 supersymmetric gauge…

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