Duality invariance in Fayet-Iliopoulos gauged supergravity

TL;DR

This paper introduces a geometric approach to identify residual symmetries in N=2, d=4 U(1) FI gauged supergravity, enabling the generation of new solutions with scalar hair and dyonic black holes from known seeds.

Contribution

It presents a novel geometric method to determine residual symmetries in FI gauged supergravity, extending solution-generating techniques to include scalar hair and dyonic black holes.

Findings

Identified residual symmetries acting on gauge couplings.

Applied method to specific models, including the F=-iX^0X^1 prepotential.

Generated a new rotating solution with scalar hair.

Abstract

We propose a geometric method to study the residual symmetries in $N=2$, $d=4$ $\text{U}(1)$ Fayet-Iliopoulos (FI) gauged supergravity. It essentially involves the stabilization of the symplectic vector of gauge couplings (FI parameters) under the action of the U-duality symmetry of the ungauged theory. In particular we are interested in those transformations that act non-trivially on the solutions and produce scalar hair and dyonic black holes from a given seed. We illustrate the procedure for finding this group in general and then show how it works in some specific models. For the prepotential $F=-iX^0X^1$, we use our method to add one more parameter to the rotating Chow-Comp\`ere solution, representing scalar hair.