Hairy Black Holes and Duality in an Extended Supergravity Model

TL;DR

This paper constructs and analyzes exact hairy black hole solutions in a specific supergravity model, exploring their duality properties and boundary conditions, with implications for dual field theories.

Contribution

It introduces two families of exact hairy black hole solutions in a gauged supergravity model and examines their duality transformations and boundary conditions.

Findings

Solutions are asymptotically AdS4.

Duality maps solutions to inequivalent families.

Boundary conditions relate to triple-trace operators in dual theory.

Abstract

We consider a $D=4$, $\mathcal{N}=2$ gauged supergravity with an electromagentic Fayet-Iliopoulos term. We restrict to the uncharged, single dilaton consistent truncation and point out that the bulk Lagrangian is self-dual under electromagnetic duality. Within this truncation, we construct two families of exact hairy black hole solutions, which are asymptotically $AdS_4$. When a duality transformation is applied on these solutions, they are mapped to two other inequivalent families of hairy black hole solutions. The mixed boundary conditions of the scalar field correspond to adding a triple-trace operator to the dual field theory action. We also show that the this truncation contains all the consistent single dilaton truncations of gauged $\mathcal{N}=8$ supergravity with a possible $\omega$-deformation.