The metric and strong coupling limit of the M5-brane

TL;DR

This work identifies a Boillat-like propagation cone for the M5-brane by introducing the 5-brane co-metric $C^{mn}$, which governs all brane fluctuations and remains inside the Einstein cone defined by $g_{mn}$. It develops a covariant framework with an energy-momentum tensor $T^{mn}=g^{mn}-C^{mn}$ that satisfies a Hooke-like elasticity relation and a Dominant Energy Condition, and demonstrates a generalized Equivalence Principle based on observables framed by $C_{mn}$. Through dimensional reduction, the authors connect the M5-brane metric to the Boillat metric of the D4-brane, and establish an open-string–like reduction consistent with known BI results. They prove exact plane-wave solutions persist nonlinearly, analyze the strong-coupling limit $T o 0$ where the theory becomes Weyl invariant and supports infinitely many conserved currents, and provide a detailed SO(5) covariant formulation with a bounded electric sector. These results illuminate the causal structure, energy conditions, and high-energy limits of M5-brane dynamics, and link them to Born–Infeld/open-string frameworks via dimensional reduction and dualities.

Abstract

We find the analogue of the Boillat metric of Born-Infeld theory for the M5-brane. We show that it provides the propagation cone of {\sl all} 5-brane degrees. In an arbitrary background field, this cone never lies outside the Einstein cone. An energy momentum tensor for the three-form is defined and shown to satisfy the Dominant Energy Condition. The theory is shown to be well defined for all values of the magnetic field but there is a limiting electric field strength. We consider the strong coupling limit of the M5-brane and show that the corresponding theory is conformally invariant and admits infinitely many conservation laws. On reduction to the Born-Infeld case this agrees with the work of Białnicki-Birula.