Abstract
We study harmonic maps from surfaces coupled to a scalar and a two-form potential, which arise as critical points of the action of the full bosonic string. We investigate several analytic and geometric properties of these maps and prove an existence result by the heat-flow method.
Highlights
Introduction and resultsHarmonic maps between Riemannian manifolds are one of the most studied variational problems in differential geometry
In the case that the domain is twodimensional harmonic maps belong to the class of conformally invariant variational problems yielding a rich structure
It is the aim of this article to study the full action of the bosonic string as a geometric variational problem
Summary
Harmonic maps between Riemannian manifolds are one of the most studied variational problems in differential geometry. The full action for the bosonic string contains two additional terms, one of them being the pullback of a two-form from the target and the other one being a scalar potential It is the aim of this article to study the full action of the bosonic string as a geometric variational problem. An existence result for harmonic maps with potential to a target with negative curvature was obtained in [12] by the heat-flow method. This result has been extended to the case of a domain manifold with boundary in [9]. We will call the critical points of the full bosonic string action harmonic maps with scalar and two-form potential and we will generalize several results already obtained for harmonic maps and harmonic maps with potential. We derive an existence result via the heat-flow method for both compact and non-compact target manifolds
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