Abstract
We study a perturbative expansion of the squashed 3-sphere \( \left({s}_b^3\right) \) 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 → 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, CT, CJJ and higher-point correlation functions of the stress-energy tensor) of the IR superconformal field theory without performing the localization integrals.
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Gang, D., Yamazaki, M. Expanding 3d \( \mathcal{N} \) = 2 theories around the round sphere. J. High Energ. Phys. 2020, 102 (2020). https://doi.org/10.1007/JHEP02(2020)102
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DOI: https://doi.org/10.1007/JHEP02(2020)102