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

Abstract

We present a family of globally regular $\mathcal{N}=1$ vacua in the D=4, $\mathcal{N}=4$ 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 $\mathcal{N}=1$ 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 $\xi \ne 0$ can be promoted to D=11 to become vacua of M-theory.

9 pages, 2 fugures