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.

This preprint was withdrawn at the authors' request due to serious scientific errors that cannot be corrected by updating the paper.

This preprint was withdrawn at the authors' request due to serious scientific errors that cannot be corrected by updating the paper.

This preprint was withdrawn at the authors' request due to serious scientific errors that cannot be corrected by updating the paper.