A Calibration Bound for the M-Theory Fivebrane

TL;DR

The paper addresses how to extend calibrations to the M-theory fivebrane in the presence of a nonzero worldvolume flux $H$ by constructing a covariant energy--momentum bound via the superembedding formalism. A fermionic field redefinition $\Psi=\Theta M$ yields a positive bound that involves the energy density $E$, momentum density $T_i{}^0$, and the dual of $H$, and the bound is saturated precisely by supersymmetric (BPS) configurations, establishing a generalized calibration characterized by closed forms $\varphi$ and $\chi$. The generalized calibration bound is $\mathcal{E} \ge \int_M {}^\star\varphi + H\wedge {}^\star\chi$, reducing to standard calibrations when $H=0$, and is compatible with dimensional reduction to D$p$-branes where the bound includes Born--Infeld field contributions. The results illuminate how worldvolume fluxes modify calibrated geometries, connect to reduced holonomy in a gauge-coupled connection, and provide a concrete framework for analyzing supersymmetric M5 solitons and their D-brane counterparts.

Abstract

We construct a covariant bound on the energy-momentum of the M-fivebrane which is saturated by all supersymmetric configurations. This leads to a generalised notion of a calibrated geometry for M-fivebranes when the worldvolume gauge field is non-zero. The generalisation relevant for Dp-branes is also given.