3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes

TL;DR

This paper explores 3d $ ext{N}=2$ SCFTs from wrapped M5-branes on hyperbolic 3-manifolds, linking their properties to complex Chern-Simons invariants, and provides numerical and bootstrap analyses of these minimal theories.

Contribution

It introduces a rigorous definition of the $SL(2)$ Chern-Simons invariant via resurgence and state-integral models, connecting geometric invariants to SCFT data.

Findings

Numerical evaluation of central charges for specific 3-manifolds.

Identification of infinitely many minimal SCFTs with small central charges.

Analysis of these SCFTs using 3d $ ext{N}=2$ bootstrap methods.

Abstract

We study CFT data of 3-dimensional superconformal field theories (SCFTs) arising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via so-called 3d/3d correspondence, central charges of these SCFTs are related to a $SL(2)$ Chern-Simons (CS) invariant on the 3-manifolds. We give a rigorous definition of the invariant in terms of resurgence theory and a state-integral model for the complex CS theory. We numerically evaluate the central charges for several closed 3-manifolds with small hyperbolic volume. The computation suggests that the wrapped M5-brane systems give infinitely many discrete SCFTs with small central charges. We also analyze these `minimal' SCFTs in the eye of 3d $\mathcal{N}=2$ superconformal bootstrap.