Towards Super Teichm\"uller Spin TQFT

TL;DR

This paper introduces the super Teichm"uller spin TQFT, extending the quantization of Teichm"uller theory to include supersymmetry, and computes its partition functions and invariants for spin 3-manifolds.

Contribution

It develops the super Teichm"uller spin TQFT, providing explicit partition functions and perturbative invariants, and explores its connections to Chern-Simons theories and M5-brane compactifications.

Findings

Explicit partition functions for super Teichm"uller spin TQFT on certain spin 3-manifolds

Perturbative invariants derived from the partition functions

Relations established with complex Chern-Simons theories and 3d N=2 theories

Abstract

The quantization of the Teichm\"uller theory has led to the formulation of the so-called Teichm\"uller TQFT for 3-manifolds. In this paper we initiate the study of "supersymmetrization" of the Teichm\"uller TQFT, which we call the super Teichm\"uller spin TQFT. We obtain concrete expressions for the partition functions of the super Teichm\"uller spin TQFT for a class of spin 3-manifold geometries, by taking advantage of the recent results on the quantization of the super Teichm\"uller theory. We then compute the perturbative expansions of the partition functions, to obtain perturbative invariants of spin 3-manifolds. We also comment on the relations of the super Teichm\"uller spin TQFT to 3-dimensional Chern-Simons theories with complex gauge groups, and to a class of 3d N=2 theories arising from the compactifications of the M5-branes.