Bogomol'nyi Equations for Einstein-Yang-Mills-Dilaton theory

TL;DR

This paper derives first-order Bogomol'nyi equations for a static, spherically symmetric Einstein-Yang-Mills-Dilaton solution, revealing a connection to supersymmetry and proposing a new Euclidean supergravity model with flat asymptotics.

Contribution

It shows that a known numerical solution satisfies Bogomol'nyi equations and introduces a novel Euclidean supergravity framework related to the equations.

Findings

Derivation of Bogomol'nyi equations for the Einstein-Yang-Mills-Dilaton system.

Identification of a link to N=4 gauged supergravity with imaginary gauge coupling.

Proposal of a new Euclidean supergravity model with asymptotically flat solutions.

Abstract

A static, spherically symmetric and purely magnetic solution of the Einstein-Yang-Mills-Dilaton theory, found previously by numerical integration is shown to obey a system of first order Bogomol'nyi equations. As common for such equations, there is a tight relation to supersymmetry, in the present case to the N=4 gauged SU(2)$\times$SU(2) supergravity of Freedman and Schwarz. Specifically, the dilaton potential of the latter can be avoided by choosing one of the two gauge coupling constants to be imaginary. It is argued that this corresponds to a hitherto unknown N=4 gauged SU(2)$\times$SU(1,1) supergravity in four Euclidean dimensions leading to Bogomol'nyi equations with asymptotically flat solutions.