Geodesic
The boundary value problem for Dirac-harmonic maps
Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 997-1031

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/384
Classification : 58-XX, 53-XX, 35-XX, 00-XX
Keywords: Dirac-harmonic map, regularity, boundary value 
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     title = {The boundary value problem for {Dirac-harmonic} maps},
     journal = {Journal of the European Mathematical Society},
     pages = {997--1031},
     publisher = {mathdoc},
     volume = {15},
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     year = {2013},
     doi = {10.4171/jems/384},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/384/}
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Qun Chen; Jürgen Jost; Guofang Wang; Miaomiao Zhu. The boundary value problem for Dirac-harmonic maps. Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 997-1031. doi: 10.4171/jems/384

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