Non-Abelian Solitons in N=4 Gauged Supergravity and Leading Order String Theory
Ali H. Chamseddine, Mikhail S. Volkov
TL;DR
Chamseddine and Volkov construct static, spherically symmetric, purely magnetic non-Abelian BPS solitons in four-dimensional N=4 gauged supergravity, identifying a 1/4-supersymmetric background with a monopole-like gauge field and globally regular geometry. They derive first-order Bogomol'nyi equations from Killing spinor constraints, revealing a one-parameter family of regular solutions that are then shown to lift to ten dimensions via a group-manifold compactification, embedding the configurations in leading-order string theory. The work establishes a concrete bridge between 4D gauged supergravity and 10D string backgrounds, with non-Abelian gauge dynamics encoded as off-diagonal metric components in ten dimensions. It also lays groundwork for future stability analyses, string-correction considerations, and extensions to other SUSY theories such as N=2.
Abstract
We study static, spherically symmetric, and purely magnetic solutions of the N=4 gauged supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/4 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. We show that the theory in which these solutions arise can be obtained via compactification of ten-dimensional supergravity on the group manifold. This result is then used to lift the solutions to ten dimensions.