World-Volume Action of the M Theory Five-Brane

TL;DR

The paper constructs a six-dimensional world-volume action for the M theory five-brane in flat 11d space with global 11d super-Poincaré symmetry and local 6d diffeomorphism and kappa symmetry. It presents two formulations: a non-covariant approach that singles out one world-volume direction and a manifestly covariant PST formulation with auxiliary fields, detailing how the self-dual tensor is incorporated and how gauge invariances are realized. Supersymmetry is added by embedding into 11d superspace, extending the Wess-Zumino structure to a closed 7-form I7, and ensuring that the full action is invariant under supersymmetry and κ-symmetry, with a careful treatment of general coordinate invariance. The work also demonstrates a consistent double dimensional reduction to a D4-brane in Type IIA, illustrating a duality between the M5-brane formulation and the reduced brane theory. Overall, the paper provides a complete classical construction of the M5-brane world-volume dynamics, its supersymmetric completion, and its relation to lower-dimensional branes via dimensional reduction, with potential implications for non-perturbative M-theory and soliton dynamics.

Abstract

This paper presents a 6d world-volume action that describes the dynamics of the M theory five-brane in a flat 11d space-time background. The world-volume action has global 11d super-Poincare invariance, as well as 6d general coordinate invariance and kappa symmetry, which are realized as local symmetries. The paper mostly considers a formulation in which general coordinate invariance is not manifest in one direction. However, it also describes briefly an alternative formulation, due to Pasti, Sorokin, and Tonin, in which general coordinate invariance is manifest. The latter approach requires auxiliary fields and new gauge invariances.