In the paper, we clarify some relations between solutions to the star-triangle equation via the gauge/YBE correspondence. We consider two solutions to the star-triangle relation in terms of Euler's gamma function. We derive these solutions from the reduction of certain basic and hyperbolic hypergeometric integral identities. These identities can be interpreted as equality of the supersymmetric partition functions of a specific three-dimensional $\mathcal{N}=2$ supersymmetric dual theories.

中文翻译：

---

星三角方程的伽马函数解

在本文中，我们通过量规/ YBE对应关系阐明了星三角方程解的一些关系。我们根据欧拉伽马函数考虑星三角关系的两种解决方案。我们从某些基本和双曲超几何积分恒等式的约简中得出这些解决方案。这些身份可以解释为特定三维的超对称分区函数的等价性$\mathcal{ñ}=2$ 超对称对偶理论。