The tale of gravitational sphaleron

Abstract

Type I string theory can be dimensionally reduced on group manifolds. The compactification on $S^3\times S^3$ leads to the N=4 gauged SU(2)$\times$SU(2) supergravity in four dimensions, which admits the BPS monopole type non-Abelian vacuum. The reduction on $S^3\times AdS_3$ gives the Euclidean N=4 gauged SU(2)$\times$SU(1,1) supergravity admitting a globally regular supersymmetric non-Abelian background. The latter can be analytically continued to the Lorentzian sector, which gives the regular, unstable particle-like configuration known as gravitational sphaleron. When lifted to D=10, the Euclidean vacuum describes a deformation of the D1--D5 brane system.