Sl(2,R)-Duality Covariance of Killing Spinors in Axion-Dilaton Black Holes

TL;DR

This paper demonstrates that $SL(2,R)$ duality invariance of dilaton-axion black holes extends to the covariance of Killing spinors, ensuring their transformation properties are consistent under duality, exemplified by explicit solutions.

Contribution

It establishes the covariance of Killing spinors under $SL(2,R)$ duality in axion-dilaton black holes, linking supersymmetry transformations with duality invariance.

Findings

Killing spinors transform covariantly under $SL(2,R)$ duality.

The invariance of the Bogomolnyi bound corresponds to supersymmetry covariance.

Explicit solutions for $SL(2,R)$-invariant axion-dilaton black holes are provided.

Abstract

Under $SL(2,R)$ electric-magnetic duality transformations the Bogomolnyi bound of dilaton-axion black holes is known to be invariant. In this paper we show that this invariance corresponds to the covariance of the $N=4$ supersymmetry transformation rules and their parameters. In particular this implies that Killing spinors transform covariantly into Killing spinors. As an example, we work out completely the case of the largest known family of axion-dilaton black holes which is $SL(2,R)$-invariant, finding the Killing spinors with the announced properties.