A Note on Topological M5-branes and String-Fivebrane Duality

TL;DR

This paper explores the stability and duality properties of topological M5-branes, deriving conditions using kappa-symmetry and linking the NS5-brane equations to the Kodaira-Spencer equation, supporting string-fivebrane duality.

Contribution

It derives stability conditions for topological M5-branes and connects NS5-brane equations to the Kodaira-Spencer equation, providing new insights into string-fivebrane duality.

Findings

Self-duality of the 3-form is consistent with stability conditions.

Double dimensional reduction yields the D4-brane, and direct reduction yields the NS5-brane.

Equation of motion for the NS5-brane's 3-form matches the Kodaira-Spencer equation.

Abstract

We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.