We study a perturbative expansion of the squashed 3-sphere ($S^3_b$) partition function of 3d $\mathcal{N}=2$ gauge theories around the squashing parameter $b= 1$. Our proposal gives the coefficients of the perturbative expansion as a finite sum over the saddle points of the supersymmetric-localization integral in the limit $b \rightarrow 0$ (the so-called Bethe vacua), and the contribution from each Bethe vacua can be systematically computed using saddle-point methods. Our expansion provides an efficient and practical method for computing basic CFT data ($F,C_T,C_{JJ}$ and higher-point correlation functions of the stress-energy tensor) of the IR superconformal field theory without performing the localization integrals.

中文翻译：

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围绕圆球展开 3d N$$ \mathcal{N} $$ = 2 理论

我们研究了压缩参数 $b=1$ 周围的 3d $\mathcal{N}=2$ 规范理论的压缩 3 球体 ($S^3_b$) 配分函数的微扰展开。我们的提议将微扰展开的系数作为极限 $b \rightarrow 0$（所谓的 Bethe vacua）中超对称定位积分的鞍点上的有限和，并且每个 Bethe vacua 的贡献可以是使用鞍点方法系统地计算。我们的扩展为计算 IR 超共形场理论的基本 CFT 数据（$F,C_T,C_{JJ}$ 和应力-能量张量的高点相关函数）提供了一种高效实用的方法，而无需执行定位积分。