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.
Highlights
Introduction and resultsThe action functional for the full bosonic string is an important model in contemporary theoretical physics
This article is a sequel to previous work concerning the existence of critical points of the full bosonic string action
In [2], an existence result was given in the case of the domain being a closed Riemannian surface and the target a Riemannian manifold having negative sectional curvature
Summary
The action functional for the full bosonic string is an important model in contemporary theoretical physics. It is defined for a map from a two-dimensional domain taking values in a manifold. This article is a sequel to previous work concerning the existence of critical points of the full bosonic string action. In [2], an existence result was given in the case of the domain being a closed Riemannian surface and the target a Riemannian manifold having negative sectional curvature. A second existence result has been established in [3] for the domain being two-dimensional Minkowski space and the target an arbitrary closed Riemannian manifold. We prove a regularity result for weak solutions of the critical points of the full bosonic string action. Mathematics Subject Classification: 58E20, 35K55, 53C80 Keywords: Full bosonic string, Heat flow, Global weak solution
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