Supersymmetric $AdS_6$ vacua in six-dimensional $N=(1,1)$ gauged supergravity

TL;DR

This paper classifies fully supersymmetric $AdS_6$ vacua in six-dimensional $N=(1,1)$ gauged supergravity, revealing the structure of the gauge group, its breaking pattern, and the absence of moduli consistent with dual 5D SCFTs.

Contribution

It provides a detailed analysis of the gauge group structure and moduli space of $AdS_6$ vacua in six-dimensional supergravity, matching holographic expectations.

Findings

Gauge group must be of the form $G'\times G''$ within $SO(4,n)$.

In vacua, gauge group breaks to $SO(3)\times H'\times H''$ with specific subgroup constraints.

No moduli preserve all supercharges, aligning with dual SCFT properties.

Abstract

We study fully supersymmetric $AdS_6$ vacua of half-maxi\-mal $N=(1,1)$ gauged supergravity in six space-time dimensions coupled to $n$ vector multiplets. We show that the existence of $AdS_6$ backgrounds requires that the gauge group is of the form $G'\times G"\subset SO(4,n)$ where $G'\subset SO(3,m)$ and $G"\subset SO(1,n-m)$. In the $AdS_6$ vacua this gauge group is broken to its maximal compact subgroup $SO(3)\times H'\times H"$ where $H'\subset SO(m)$ and $H"\subset SO(n-m)$. Furthermore, the $SO(3)$ factor is the R-symmetry gauged by three of the four graviphotons. We further show that the $AdS_6$ vacua have no moduli that preserve all supercharges. This is precisely in agreement with the absence of supersymmetric marginal deformations in holographically dual five-dimensional superconformal field theories.