Killing Spinors for Finite Temperature Euclidean Solutions at the BPS Bound

TL;DR

This paper explicitly constructs Killing spinors for finite temperature Euclidean BPS solutions in five-dimensional supergravity, confirming their supersymmetry and analyzing charge distributions.

Contribution

It provides the first explicit construction of Killing spinors for these finite temperature BPS solutions, extending previous theoretical conjectures.

Findings

Killing spinors are explicitly constructed for the solutions.

The total charge divides into two harmonic sources on flat space.

The solutions are confirmed to be supersymmetric at finite temperature.

Abstract

In a recent paper [arXiv:2308.00038], Anupam, Chowdhury, and Sen conjectured that the finite temperature Euclidean five-dimensional Cvetic-Youm solution saturating the BPS bound is supersymmetric. In this paper, we explicitly construct Killing spinors for this solution in five-dimensional minimal supergravity. We also expand on the previous discussions of Killing spinors for the finite temperature Euclidean Kerr-Newman solution saturating the BPS bound. For both these cases, we show that the total charge gets divided into two harmonic sources on three-dimensional flat base space.