Deformation of Curved BPS Domain Walls and Supersymmetric Flows on 2d Kähler-Ricci Soliton

Some aspects of curved BPS domain walls and their supersymmetric Lorentz invariant vacuums of four dimensional N = 1 supergravity coupled to a chiral multiplet are considered. In particular, the scalar manifold can be viewed as two dimensional Kähler-Ricci soliton which further implies that all quantities describing the walls and their vacuums have evolution with respect to the soliton. Then, the analysis using BPS equations results a lower bound which leads to a restriction of the vacuums related to field theory on curved background. Furthermore, in order to verify their existence in ultraviolet or infrared regions one has to perform the renormalization group analysis. Finally, a simplest model with linear superpotential and the Kähler-Ricci soliton considered as Rosenau solution is discussed in detail. email: [email protected], [email protected]