Comments on supersymmetric solutions of minimal gauged supergravity in five dimensions

TL;DR

This paper explores supersymmetric solutions in five-dimensional minimal gauged supergravity, proposing a new ansatz that simplifies the problem to a single sixth-order equation, leading to a novel analytic solution with potential implications for dual field theories.

Contribution

It introduces a new ansatz based on orthotoric Kaehler metrics, reducing the problem to a single sixth-order equation, and finds a new analytic asymptotically AdS solution with five parameters.

Findings

Derived a sixth-order equation for two functions of one variable.

Found a new five-parameter asymptotically AdS solution.

Identified a unique regular topological soliton within the solution family.

Abstract

We investigate supersymmetric solutions of minimal gauged supergravity in five dimensions, in the timelike class. We propose an ansatz based on a four-dimensional local orthotoric Kaehler metric and reduce the problem to a single sixth-order equation for two functions, each of one variable. We find an analytic, asymptotically locally AdS solution comprising five parameters. For a conformally flat boundary, this reduces to a previously known solution with three parameters, representing the most general solution of this type known in the minimal theory. We discuss the possible relevance of certain topological solitons contained in the latter to account for the supersymmetric Casimir energy of dual superconformal field theories on S^3 x R. Although we obtain a negative response, our analysis clarifies several aspects of these solutions. In particular, we show that there exists a unique regular topological soliton in this family.