The geometry of the M5-branes and TQFTs

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.

17+1 pages, LaTeX file; v2 misprints corrected and clarifications added, final version to appear in Journal of Geometry and Physics

References in corpus (3)

• Killing Spinors and SYM on Curved Spaces
• Area law corrections from state counting and supergravity
• Microscopic entropy of the most general four-dimensional BPS black hole

Cited by in corpus (8)

• Time-Dependent Warping, Fluxes, and NCYM
• Exact results for $\mathcal{N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
• The partition bundle of type A_{N-1} (2, 0) theory
• $S$-duality in Vafa-Witten theory for non-simply laced gauge groups
• Supersymmetric Heterotic Action out of M5 Brane
• An Approach to $\mathcal{N}=4$ ADE Gauge Theory on K3
• The M5-brane on K3 x T^2
• Hecke Operator and S-Duality of N=4 Super Yang-Mills for ADE Gauge Group on K3