# Nonlinear symmetries of black hole entropy in gauged supergravity

## TL;DR

This paper extends Freudenthal duality, originally a symmetry in ungauged supergravity, to gauged supergravity with hypermultiplets, showing it as a nonlinear symmetry of black hole entropy.

## Contribution

It generalizes Freudenthal duality to the gauged supergravity case, demonstrating its role as a nonlinear symmetry of black hole entropy with explicit model examples.

## Key findings

- Freudenthal duality can be extended to gauged supergravity.
- The duality preserves scalar field values at the black hole horizon.
- Explicit invariance shown for a specific supergravity model.

## Abstract

Freudenthal duality in N=2, D=4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy. We explicitly show this invariance for the model with prepotential $F=-i X^0 X^1$ and Fayet-Iliopoulos gauging.