Symmetric Potentials of Gauged Supergravities in Diverse Dimensions and Coulomb Branch of Gauge Theories

TL;DR

This paper explores a class of scalar field geometries in gauged supergravity, derived from brane distributions, revealing their structure, origins, and fluctuation spectra in the context of the AdS/CFT correspondence.

Contribution

It introduces new conformally flat, asymptotically AdS geometries with scalar profiles from consistent truncations of higher-dimensional brane systems, expanding understanding of Coulomb branch states.

Findings

Geometries descend from D-brane distributions in string/M-theory.

Spectra of scalar fluctuations include both discrete and continuous parts.

All solutions relate to Coulomb branch states in dual conformal field theories.

Abstract

A class of conformally flat and asymptotically anti-de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parameterise the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS_6 which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from massive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluctuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.