Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere

Abstract

We study a perturbative expansion of the squashed 3-sphere ($S_b^3$) 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 $b\to 0$ (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.

arXiv comment30 pages

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• Disordered vector models: from higher spins to incipient strings
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• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Compactifying 5d superconformal field theories to 3d
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• Three Dimensional Topological Field Theories and Nahm Sum Formulas