SUPERGRAVITY DOMAIN-WALLS

We review the status of domain walls in N=1 supergravity theories for the vacuum domain walls as well as dilatonic domain walls. We concentr ate on a systematic analysis of the nature of the space-time in these domain wall backgrounds and the special role that supersymmetry is pla ying in determining the nature of such configurations. Isotropic vacuu m domain walls that can exist between isolated minima of an N=1 superg ravity matter potential fall into three classes: (i) extreme walls, wh ich are static planar walls between supersymmetric minima, (ii) non-ex treme walls, which are expanding bubbles with two centres and (iii) ul tra-extreme walls, which are bubbles of false vacuum decay. Dilatonic walls arise in N=1 supergravity with a general coupling of the linear supermultiplet. The dilaton field, a scalar component of the linear mu ltiplet, has no perturbative self-interaction, but couples to the matt er potential responsible for the formation of the wall. The dilaton dr astically changes the global space-time properties of the wall. For th e extreme ones the spacetime structure depends on the strength of the dilaton coupling, while for non- and ultra-extreme solutions one alway s encounters naked singularities (in the absence of non-perturbative c orrections to the dilaton potential). Non-perturbative effects may mod ify the dilaton coupling so that it has a discrete non-compact symmetr y (S-duality). In this case the non-and ultra-extreme solutions can re duce to the singularity-free vacuum domain wall solutions. We also sum marize domain wall configurations within the effective theory of N=1 s uperstring vacua, with and without inclusion of non-perturbative strin g effects, and also provide a comparison with other topological defect s of perturbative string vacua.