Three-Dimensional Topological Field Theories and Non-Unitary Minimal Models

TL;DR

This paper uncovers a connection between 3D non-unitary topological field theories derived from twisted superconformal theories and 2D non-unitary minimal models, providing new insights into their structure and properties.

Contribution

It establishes a novel correspondence between topologically twisted 3D ${ m N}=4$ SCFTs and Virasoro minimal models, with explicit calculations of partition functions and characters.

Findings

Reproduces minimal model characters and modular matrices from 3D TFTs.

Provides UV descriptions with manifest ${ m N}=2$ supersymmetry.

Suggests a broader link between 3D ${ m N}=4$ SCFTs and 2D non-unitary rational CFTs.

Abstract

We find an intriguing relation between a class of 3-dimensional non-unitary topological field theories (TFTs) and Virasoro minimal models $M(2,2r+3)$ with $r \geq 1$. The TFTs are constructed by topologically twisting $3d$ ${\mathcal N}=4$ superconformal field theories (SCFTs) of rank-0, i.e. having zero-dimensional Coulomb and Higgs branches. We present ultraviolet (UV) field theory descriptions of the SCFTs with manifest ${\mathcal N}=2$ supersymmetry, which we argue is enhanced to ${\mathcal N}=4$ in the infrared. From the UV description, we compute various partition functions of the TFTs and reproduce some basic properties of the minimal models, such as their characters and modular matrices. We expect more general correspondence between topologically twisted $3d$ ${\mathcal N}=4$ rank-0 SCFTs and $2d$ non-unitary rational conformal field theories.