Expanding 3d N=2 theories around the round sphere

We study a perturbative expansion of the squashed 3-sphere partition function of 3d 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, 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.