Regular non-Abelian vacua inN=4,SO(4)gauged supergravity

Abstract

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