Bogomolʹnyi equations for Einstein-Yang-Mills-dilaton theory Original Research Article

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 Bogomolʹnyi equations. As common for such equations, there is a tight relation to supersymmetry, in the present case to the N = 4 gauged SU(2) × 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) × SU(1,1) supergravity in four Euclidean dimensions leading to Bogomolʹnyi equations with asymptotically flat solutions.