A global weak solution to the full bosonic string heat flow

TL;DR

This paper establishes the existence and properties of global weak solutions to the full bosonic string heat flow, including convergence and critical point existence, under specific smallness conditions on geometric data.

Contribution

It provides the first proof of global weak solutions for the full bosonic string heat flow with convergence analysis and critical point existence results.

Findings

Existence of unique global weak solutions under smallness conditions.

Solutions are smooth except at finitely many singular points.

Convergence of the heat flow and new existence results for critical points.

Abstract

We prove the existence of a unique global weak solution to the full bosonic string heat flow from closed Riemannian surfaces to an arbitrary target under smallness conditions on the two-form and the scalar potential. The solution is smooth with the exception of finitely many singular points. Finally, we discuss the convergence of the heat flow and obtain a new existence result for critical points of the full bosonic string action.