The geometry of M5-branes and TQFTs

Abstract

The calculation of the partition function for N M5-branes is addressed for the case in which the world-volume wraps a manifold T 2× 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 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.