The geometry of the M5-branes and TQFTs

TL;DR

This paper explores the geometric aspects of M5-branes wrapped on specific manifolds, connecting M-theory compactifications to Vafa-Witten theory and algebraic moduli space classification.

Contribution

It provides a novel geometric framework linking M5-brane partition functions to spectral cover moduli space classification in a specific compactification setting.

Findings

Partition function calculation for M5-branes on T^2 x M_4.

Reduction of moduli counting to algebraic equations.

Connection between BPS spectrum and spectral covers.

Abstract

The calculation of the partition function for N M5-branes is addressed for the case in which the worldvolume wraps a manifold $T^2\times M_4$, where $M_4$ is simply connected and Kaehler. This is done in a compactification of M-theory which induces the Vafa-Witten theory on $M_4$ in the limit of vanishing torus volume. The results follow from the equivalence of the BPS spectrum counting in the complementary limit of vanishing $M_4$ volumes and from a classification of the the moduli space of quantum vacua of the supersymmetric twisted theory in terms of associated spectral covers. This reduces the problem of the moduli counting to algebraic equations.