A global weak solution to the full bosonic string heat flow

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.