Abstract
We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely many singularities. Moreover, we discuss the convergence of the evolution equations and address the question if we can remove the regularization in the end.
Highlights
Introduction and ResultsHarmonic maps from Riemannian surfaces to Riemannian manifolds are a variational problem with rich structure
Diracharmonic maps still belong to the class of conformally invariant variational problems
Dirac-harmonic maps coupled to a two-form potential, called Magnetic Diracharmonic maps, are studied in [5] and Dirac-harmonic maps to manifolds with torsion are examined in [7]
Summary
Harmonic maps from Riemannian surfaces to Riemannian manifolds are a variational problem with rich structure. Due to their conformal invariance the latter share a lot of special properties. The existence of harmonic maps from surfaces has been established by several methods. An extension of harmonic maps motivated from supersymmetric field theories in physics are Dirac-harmonic maps introduced in [17]. These arise as critical points of an action functional and couple the equation for harmonic maps with spinor fields.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
