Flat Bogomolnyi-Prasad-Sommerfeld domain walls on two-dimensional Kaehler-Ricci soliton

In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of four-dimensional N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of two-dimensional Kaehler manifolds satisfying a Kaehler-Ricci flow equation. We find that BPS equations and the scalar potential deform with respect to the real parameter related to the Kaehler-Ricci soliton. In addition, the analysis using gradient and renormalization group flows is carried out to ensure the existence of Lorentz invariant vacua related to anti-de Sitter/conformal field theory correspondence.