Supersymmetric AdS_6 Solutions of Type IIB Supergravity

TL;DR

This paper characterizes supersymmetric AdS_6 solutions in type IIB supergravity using Killing spinors, confirms previous pure spinor results, and derives a related four-dimensional nonlinear sigma model with scalar fields and a potential.

Contribution

It provides a detailed analysis of supersymmetric AdS_6 solutions in type IIB supergravity and derives the associated four-dimensional effective theory with scalar fields and potential.

Findings

Agreement with previous pure spinor work

Explicit form of Killing spinor bilinears

Derivation of a four-dimensional sigma model with scalar potential

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.