Timelike structures of ten-dimensional supersymmetry

TL;DR

This paper introduces a new system of equations in ten-dimensional supergravity that captures supersymmetry through calibrations, including D-branes, NS5-branes, and KK5-monopoles, assuming a timelike Killing vector.

Contribution

It provides a unified calibration-based framework for supersymmetry in type II supergravity without spacetime factorization assumptions.

Findings

Includes NS5-brane and KK5-monopole calibrations

Provides a manifestly S-invariant system

Applies to near-horizon backgrounds

Abstract

In several contexts, supersymmetry can be reformulated in terms of calibrations, namely forms whose integrals measure minimal energies. It has been conjectured that this should be possible in general. For type II supergravity, we present a new system of equations which realizes this expectation. Besides the customary D-brane calibrations, it also includes NS5-brane and KK5-monopole calibrations. It is equivalent to supersymmetry under the assumption that the Killing vector associated to supersymmetry is timelike. No assumption is made on a factorization of spacetime. We also obtain a version of the system which is manifestly S-invariant and we present an application to near-horizon backgrounds. Using calibration, a definition of central charges in purely gravitational terms is given.