The boundary value problem for Dirac-harmonic maps
TLDR
In this paper, the analytic regularity of Dirac-harmonic maps is studied in a geometric framework, including the appropriate boundary conditions, and it is shown that a weakly Diracharmonic map is smooth in the interior of the domain.Abstract:
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 Diracharmonic 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.read more
Citations
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Regularity at the free boundary for Dirac-harmonic maps from surfaces
Ben Sharp,Miaomiao Zhu +1 more
TL;DR: In this paper, the authors established the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints, and proved full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces.
Journal ArticleDOI
The maximum principle and the Dirichlet problem for Dirac-harmonic maps
TL;DR: In this article, the authors established a maximum principle and uniqueness for Dirac-harmonic maps from a Riemannian spin manifold with boundary into a regular ball in any N-mani-fold manifold.
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Some aspects of Dirac-harmonic maps with curvature term
TL;DR: In this paper, several geometric and analytic aspects of Dirac-harmonic maps with curvature term from closed Riemannian surfaces were studied, and the curvature terms were analyzed.
Journal ArticleDOI
Dirac-harmonic maps with torsion
TL;DR: In this paper, the authors studied Dirac-harmonic maps from surfaces to manifolds with torsion, motivated from the superstring action considered in theoretical physics, and discussed analytic and geometric properties of such maps and outline an existence result for uncoupled solutions.
References
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Spectral Asymmetry and Riemannian Geometry
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