On the generalized Komar charge of supersymmetric solutions

TL;DR

This paper demonstrates that the generalized Komar charges for supersymmetric solutions in various supergravity theories vanish, providing a coordinate-independent proof of BPS bounds.

Contribution

It establishes that the generalized Komar charges vanish for supersymmetric solutions, enabling a rigorous proof of BPS bounds across multiple supergravity models.

Findings

Generalized Komar charges vanish for supersymmetric solutions.

This property aids in proving BPS bounds rigorously.

Applicable to several supergravity theories, including ungauged $ abla=2$ and $ abla=1$ models.

Abstract

We consider the supersymmetric solutions of several supergravity theories (ungauged $\mathcal{N}=2,d=4$ and $\mathcal{N}=1,d=5$ supergravities coupled to vector supermultiplets and pure $\mathcal{N}=1,d=10$ supergravity) and show that their generalized Komar charges vanish identically for the supersymmetric Killing vector which is constructed as a bilinear of the Killing spinors of those solutions. This property can be used to prove the supersymmetry (``BPS'') bounds satisfied by some of those solutions in a rigorous, coordinate-independent way.