Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

Abstract

A theory of nonassociative geometric flows is formulated as an extension of a string‐inspired model of nonassociative gravity determined by star product. The nonassociative Ricci tensor and curvature scalar defined by (non) symmetric metric structures and generalized (non) linear connections are used for defining nonassociative versions of Grigori Perelman F‐ and W‐functionals for Ricci flows and computing associated thermodynamic variables. The anholonomic frame and connection deformation method, AFCDM, which allows us to construct exact and parametric solutions describing nonassociative geometric flow evolution scenarios and modified Ricci soliton configurations with quasi‐stationary generic off‐diagonal metrics are developed and applied. There are provided explicit examples of solutions modeling geometric and statistical thermodynamic evolution on a temperature‐like parameter of modified black hole configurations encoding nonassociative star‐product and R‐flux deformation data. Further perspectives of the paper are motivated by nonassociative off‐diagonal geometric flow extensions of the swampland program, related conjectures and claims on geometric and physical properties of new classes of quasi‐stationary Ricci flow and black hole solutions.