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MiS Preprint

The boundary value problem for Dirac-harmonic maps

Qun Chen, Jürgen Jost, Guofang Wang and Miaomiao Zhu


Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We show that a weakly Dirac-harmonic map is smooth in the interior of the domain. We also prove regularity results for Dirac-harmonic maps at the boundary when they solve an appropriate boundary value problem which is the mathematical interpretation of the D-branes of superstring theory.

MSC Codes:
58E20, 53C43, 53C27
Dirac-harmonic map, regularity, boundary value

Related publications

2013 Repository Open Access
Qun Chen, Jürgen Jost, Guofang Wang and Miaomiao Zhu

The boundary value problem for Dirac-harmonic maps

In: Journal of the European Mathematical Society, 15 (2013) 3, pp. 997-1031