The M5-brane Hamiltonian

TL;DR

The paper derives the Hamiltonian form of the M5-brane worldvolume action in general $D=11$ supergravity backgrounds using the PST formalism to handle the self-dual 3-form, revealing a canonical structure with linear, second-class self-duality constraints. It then explores promoting the brane tension $T$ to a dynamical variable, obtaining a covariant Lagrangian with a 5-form gauge potential $A^{(5)}$ and a modified field strength $G$, but identifies on-shell singularities and limitations that prevent a fully satisfactory equivalence with the original action, especially in the tensionless limit. The authors find that the zero-tension limit effectively reduces to the standard null M5-brane unless restrictive conditions are imposed, and argue that the dynamical-tension formulation is not compelling from a physical standpoint, given the absence of brane-ending on M5 and related domain-wall considerations for NS5 branes. Overall, the work clarifies the interplay between Hamiltonian structure, background isometries, and covariant versus non-covariant formulations of the M5-brane.

Abstract

We obtain the Hamiltonian form of the worldvolume action for the M5-brane in a general D=11 supergravity background. We use this result to obtain a new version of the covariant M5-brane Lagrangian in which the tension appears as a dynamical variable, although this Lagrangian has some unsatisfactory features which we trace to peculiarities of the null limit. We also show that the M5-brane action is invariant under all (super)isometries of the background.