4d F(4) gauged supergravity and black holes of class $\mathcal{F}$

TL;DR

This paper reduces 6d F(4) supergravity to 4d, constructs dyonic black holes, and explores their holographic duals and entropy, revealing new solutions and insights into class F superconformal theories.

Contribution

It provides the first explicit construction of dyonic AdS$_6$ black holes and connects them to 3d class $ ext{F}$ SCFTs via a detailed supergravity reduction and duality analysis.

Findings

Constructed static dyonic black holes in AdS$_6$.

Performed microscopic entropy counting using 5d topologically twisted index.

Found new AdS$_4$ solutions predicting SCFT partition functions.

Abstract

We perform a consistent reduction of 6d matter-coupled F(4) supergravity on a compact Riemann surface $\Sigma_\mathfrak{g}$ of genus $\mathfrak{g}$, at the level of the bosonic action. The result is an $\mathcal{N}=2$ gauged supergravity coupled to two vector multiplets and a single hypermultiplet. The four-dimensional model is holographically dual to the 3d superconformal field theories of class $\mathcal{F}$, describing different brane systems in massive type IIA and IIB wrapped on $\Sigma_\mathfrak{g}$. The naive reduction leads to a non-standard 4d mixed duality frame with both electric and magnetic gauge fields, as well as a massive tensor, that can be only described in the embedding tensor formalism. Upon a chain of electromagnetic dualities, we are able to determine the scalar manifolds and electric gaugings that uniquely specify the model in the standard supergravity frame. We then use the result to construct the first examples of static dyonic black holes in AdS$_6$ and perform a microscopic counting of their entropy via the 5d topologically twisted index. Finally, we show the existence of further subtruncations to the massless sector of the 4d theory, such as the Fayet-Iliopoulos gauged $T^3$ model and minimal gauged supergravity. We are in turn able to find new asymptotically AdS$_4$ solutions, providing predictions for the squashed $S^3$ partition functions and the superconformal and refined twisted indices of class $\mathcal{F}$ theories.