Stability of Vacua and Domain Walls in Supergravity and Superstring Theory

TL;DR

This paper demonstrates that in N=1 supergravity theories, supersymmetric vacua are absolutely stable against decay into other vacua, with no static spherical domain walls existing, but planar walls can interpolate between different supersymmetric vacua.

Contribution

It establishes a Bogomol'nyi bound for domain wall energy density, proving stability of supersymmetric vacua and clarifying the existence of planar but not spherical domain walls.

Findings

Supersymmetric vacua are stable against false vacuum decay.

No static spherical domain walls exist between supersymmetric vacua.

Planar domain walls can interpolate between Minkowski and AdS vacua.

Abstract

We address the possibility of false vacuum decay in $N=1$ supergravity theories, including those corresponding to superstring vacua. By establishing a Bogomol'nyi bound for the energy density stored in the domain wall of the $O(4)$ invariant bubble, we show that supersymmetric vacua remain absolutely stable against false vacuum decay into another supersymmetric vacuum, including those from a Minkowski to an anti-deSitter (AdS) one. As a consequence, there are no compact static spherical domain walls, while on the other hand there exist planar domain walls interpolating between non-degenerate supersymmetric vacua, e.g. between Minkowski (topology $\Re^{4}$) and AdS (topology $S^{1}(time) \times \Re^{3}(space)$) vacua. (Talk presented at the XXVI International Conference on High Energy Physics August 6-12, 1992, Dallas, Texas)