Supergravity Domain Walls

TL;DR

This review surveys domain walls in $N=1$ supergravity, focusing on vacuum and dilatonic walls and the crucial role of supersymmetry in shaping their spacetime structure. It develops a unified framework—the isotropic thin-wall formalism with Israel junction conditions and a Bogomol'nyi bound—to classify extreme, non-extreme, and ultra-extreme walls, and to derive their global geometries and stability properties. Extreme vacuum walls saturate a SUSY bound and exhibit balanced AdS/Minkowski regions with zero Tolman mass, while non-extreme and ultra-extreme walls generally feature dynamic, horizon-rich spacetimes and often naked singularities, reflecting the delicate balance of wall tension, dilaton energy, and cosmological constants. The dilatonic sector introduces further richness: extreme dilatonic walls depend sensitively on the dilaton coupling $\alpha$, with naked singularities arising for $\alpha>1$ and special behavior at $\alpha=1$ (stringy coupling). The paper then connects these four-dimensional domain-wall configurations to string theory, highlighting complementarity with BPS black holes in $N=4$ vacua, and discusses how perturbative and non-perturbative effects in string vacua can realize or constrain wall solutions, with implications for early-universe cosmology and SUSY breaking.

Abstract

We review the status of domain walls in $N=1$ supergravity theories for both the vacuum domain walls as well as dilatonic domain walls. We concentrate on a systematic analysis of the nature of the space-time in such domain wall backgrounds and the special role that supersymmetry is playing in determining the nature of such configurations.

Figures (25)

• Figure 1: The double-well potential of Eq. (\ref{['Eq:DoubleWell']}).
• Figure 2: The kink solution $\phi_{+}$ of Eq. (\ref{['Eq:KinkSolution']}).
• Figure 3: The spatial coordinates in the wall space--time; $z$ describes the direction orthogonal to the wall surface.
• Figure 4: Two-dimensional analogue of the spatial section of the geodesically complete Vilenkin domain wall (domain wall between Minkowski vacua) space--time. The whole spatial geometry is the closed surface (to the left), and the domain string (the analogue of a domain wall in three dimensions) is the dividing circle depicted on the right. Note that angular circles decrease on both sides of the string: both sides are inside the circular domain string.
• Figure 5: The metric conformal factor as function of the distance from the wall (at the origin) for extreme domain walls of Type I, II, and III, respectively .