Supersymmetric AdS_6 Solutions of Type IIB Supergravity

TL;DR

The paper advances the classification of supersymmetric AdS$_6$ solutions in type IIB supergravity by applying a Killing spinor framework to derive a canonical metric-flux form that matches prior pure spinor results, and by extracting a four-dimensional effective action via AdS$_6$ dimensional reduction. It reveals a nonlinear sigma model with five scalars parametrizing the coset $\text{SL}(3,\mathbb{R})/\text{SO}(2,1)$, supplemented by a scalar potential realized through the non-semi-simple gauging CSO$(1,1,1)$, analogous to gauged supergravity constructions. The analysis identifies an $SU(2)$ isometry corresponding to the $S^2$ factor and constructs the full fluxes and warp factors in terms of two coupled PDEs for $U$ and $\phi$, consistent with Apruzzi et al. The 4D action and coset structure provide a useful framework for locating explicit AdS$_6$ solutions and for exploring potential dual 5D SCFTs, including connections to brane webs and generalized gauging schemes.

Abstract

We study the general requirement for supersymmetric AdS$_6$ solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the canonical form of the solutions. Our result agrees precisely with the work of Apruzzi et. al. \cite{Apruzzi:2014qva} which used the pure spinor technique. We also obtained the four-dimensional theory through the dimensional reduction of type IIB supergravity on AdS$_6$. This effective action is essentially a nonlinear sigma model with five scalar fields parametrizing $\textrm{SL}(3,\mathbb{R})/\textrm{SO}(2,1)$, modified by a scalar potential and coupled to Einstein gravity in Euclidean signature. We argue that the scalar potential can be explained by a subgroup CSO(1,1,1) $\subset\textrm{SL}(3,\mathbb{R})$ in a way analogous to gauged supergravity.