Domain Walls and Massive Gauged Supergravity Potentials

Abstract

We point out that massive gauged supergravity potentials, for example those arising due to the massive breathing mode of sphere reductions in M-theory or string theory, allow for supersymmetric (static) domain wall solutions which are a hybrid of a Randall-Sundrum domain wall on one side, and a dilatonic domain wall with a run-away dilaton on the other side. On the anti-de Sitter (AdS) side, these walls have a repulsive gravity with an asymptotic region corresponding to the Cauchy horizon, while on the other side the runaway dilaton approaches the weak coupling regime and a non-singular attractive gravity, with the asymptotic region corresponding to the boundary of spacetime. We contrast these results with the situation for gauged supergravity potentials for massless scalar modes, whose supersymmetric AdS extrema are generically maxima, and there the asymptotic regime transverse to the wall corresponds to the boundary of the AdS spacetime. We also comment on the possibility that the massive breathing mode may, in the case of fundamental domain-wall sources, stabilize such walls via a Goldberger-Wise mechanism.

Figures (3)

• Figure 1: The scalar potential (\ref{['scalarpot']}) as a function of $\phi$ for the $D=5$ case. The structure of the potential for other dimensions is similar.
• Figure 2: The functions $e^{2A}$ (upper line) and $\phi$ (lower line) for $D=5$ as functions of the transverse coordinate $z$. Their forms for other dimensions are similar.
• Figure 3: The metric functions $e^{2A}$ (upper) and $\phi$ (lower) as a function of the transverse direction $z$ with the domain wall source added by hand. The solution provides a realization of the Goldberger-Wise GW mechanism, where the massive breathing mode provides a potential that stabilizes the domain wall source and relaxes asymptotically to the AdS minimum of the potential.