Supersymmetry and generalized calibrations

TL;DR

The paper shows that static minimal-energy configurations of super $p$-branes in supersymmetric backgrounds are governed by generalized calibrations, extending the traditional calibration concept to cases with nonzero worldvolume electrostatic terms via the relation $d\varphi = -d(i_kA)$. It derives the generalized calibration bound from the p-brane supersymmetry algebra and κ-symmetry, tying preserved supersymmetry to eigenmodes of a projection operator and to saturating energy bounds. The authors provide extensive M-brane examples in varied backgrounds, including hermitian, SAS, and exceptional calibrations for M2- and M5-branes, yielding holomorphic, almost-symplectic, and Spin(7)/G2-structured calibrated submanifolds with explicit energy bounds and SUSY fractions. The work offers a unified geometric framework for understanding brane intersections and worldvolume solitons, and it points toward broader applicability to D-branes and duality chains, while noting limitations when extra worldvolume fields are active.

Abstract

A static minimal energy configuration of a super p-brane in a supersymmetric (n+1)-dimensional spacetime is shown to be a `generalized calibrated' submanifold. Calibrations in $\bE^{(1,n)}$ and $AdS_{n+1}$ are special cases. We present several M-brane examples.