Flat world of dilatonic domain walls.

We study dilatonic domain walls specific to superstring theory. Along with the matter fields and metric the dilaton also changes its value in the wall background. We found supersymmetric (extreme) solutions which in general interpolate between isolated superstring vacua with non-equal value of the matter potential; they correspond to the static, planar domain walls with flat metric in the string (sigma model) frame. We point out similarities between the space-time of dilatonic walls and that of charged dilatonic black holes. We also comment on non-extreme solutions corresponding to expanding bubbles. PACS # 11.17+y, 04.20.-q, 04.65.+e, 11.30.Pb We address dilatonic domain wall solutions 1 which are specific to superstring theory. In the domain wall background along with the matter fields and metric the dilaton field also changes its value. Such walls are of particular interest because they correspond to configurations which interpolate between isolated superstring vacua and may thus shed light on the nature and connectedness of the superstring vacua. The primary goal is to present supersymmetric (extreme) solutions which correspond to static, planar domain walls in general interpolating between isolated four dimensional (4d) superstring vacua with non-equal value of the matter potential. We also comment on non-extreme walls. Dilatonic domain walls are a generalization of the “ordinary” domain walls 2,3 in an analogous way as dilatonic charged black holes 10,11 are a generalization of “ordinary” black holes. Ordinary domain walls between vacua of non-equal cosmological constant fall into three classes: 4 (i) extreme (supersymmetric) static, planar domain walls, 5,6,7,8,9 (ii) non-extreme domain walls (expanding bubbles with an inertial observer inside the bubble for each side of the wall) 4,3 and (iii) ultra-extreme walls (expanding bubbles 12,13 of false vacuum decay 14 ). The energy density σultra non of the non[or ultra-]extreme walls is bound from below [or above] by the one σext of the extreme ones. Walls are thus an example 4 of configurations for which supersymmetry provides a lower bound for the energy of stable wall configurations. 15 The space-times induced by the walls are non-singular with non-trivial global structure and horizons closely related to the ones of certain black holes: on the anti-deSitter [or Minkowski] side of the wall the induced non-singular spacetime is closely related to the ones of the Reissner-Nordström [or Schwarzschild] black holes. 4 The intriguing similarity between the space-time of the walls and the one of the corresponding black-holes reappears in the case of dilatonic walls as well.