Coupled Ricci–Dilaton–Flux Flows in String Theory

Westudy coupled geometric flows involving the metric, dilaton, and flux fields arising from worldsheet β-functions in string theory. Extending the Ricci flow formalism, we derive parabolic evolution equations governing these fields and prove short-time exis tence and uniqueness for SU(3)-structure compactifications. We establish monotonicity properties of flow functionals analogous to Perelman’s entropy and identify conditions for moduli stabilization in type II backgrounds. Our results unify Ricci-type flow techniques with flux compactifications and suggest new mathematical tools for analyzing dynamical string backgrounds and quantum gravity.