4D N = 1 Supersymmetric Yang-Mills Theories on Kahler-Ricci Soliton

In this study we consider four dimensional N = 1 supersymmetric gauge Yang-Mills theory whose complex scalar manifold is Kahler and deforms with respect to a real parameter. The deformation of the geometry is governed by Kahler-Ricci flow equation. This setup implies that some couplings such as shifting quantities, momentum maps and the scalar potential turn out to be evolved with respect to the flow parameter. We also discuss deformation of vacuum structures of the theory in the context of Morse theory.