Supergravity Domain Walls

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 rôle that supersymmetry is playing in determining the nature of such configurations. Isotropic vacuum domain walls that can exist between isolated minima of a N = 1 supergravity matter potential fall into three classes: (i) extreme walls which are static planar walls between supersymmetric minima, (ii) non-extreme walls which are expanding bubbles with two centres and (iii) ultra-extreme walls which are bubbles of false vacuum decay. Dilatonic walls arise in N = 1 supergravity with the linear supermultiplet, an additional scalar field-the dilatonhas no perturbative self-interaction, which however, couples to the matter potential responsible for the formation of the wall. The dilaton drastically changes the global space–time properties of the wall. For the extreme ones the space–time structure depends on the strength of the dilaton coupling, while for nonand ultra-extreme solutions one always encounters naked singularities (in the absence of non-perturbative corrections to the dilaton potential). Non-perturbative effects may modify the dilaton coupling so that it has a discrete non-compact symmetry (S-duality). In this case the nonand ultra-extreme solutions can reduce to the singularity-free vacuum domain wall solutions. We also summarize domain wall configurations within effective theory of N = 1 superstring vacua, with or without inclusion of non-perturbative string effects, and also provide a comparison with other topological defects of perturbative string vacua. On sabbatical leave from Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396, U.S.A.