Regular non-Abelian vacua in ${\cal N}=4$, SO(4) gauged supergravity

Abstract

We present a family of globally regular ${\cal N}=1$ vacua in the D=4, ${\cal N}=4$ gauged supergravity of Gates and Zwiebach. These solutions are labeled by the ratio $\xi$ of the two gauge couplings, and for $\xi=0$ they reduce to the supergravity monopole previously used for constructing the gravity dual of ${\cal N}=1$ super Yang-Mills theory. For $\xi>0$ the solutions are asymptotically anti de Sitter, but with an excess of the solid angle, and they reduce exactly to anti de Sitter for $\xi=1$. Solutions with $\xi<0$ are topologically $R^1\times S^3$, and for $\xi=-2$ they become $R^1\times S^3$ geometrically. All solutions with $\xi\neq 0$ can be promoted to D=11 to become vacua of M-theory.