# The boundary value problem for Dirac-harmonic maps

Qun Chen; Jürgen Jost; Guofang Wang; Miaomiao Zhu

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 3, page 997-1031
- ISSN: 1435-9855

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topChen, Qun, et al. "The boundary value problem for Dirac-harmonic maps." Journal of the European Mathematical Society 015.3 (2013): 997-1031. <http://eudml.org/doc/277200>.

@article{Chen2013,

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 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.},

author = {Chen, Qun, Jost, Jürgen, Wang, Guofang, Zhu, Miaomiao},

journal = {Journal of the European Mathematical Society},

keywords = {Dirac-harmonic map; regularity; boundary value; Dirac-harmonic map; regularity; boundary value},

language = {eng},

number = {3},

pages = {997-1031},

publisher = {European Mathematical Society Publishing House},

title = {The boundary value problem for Dirac-harmonic maps},

url = {http://eudml.org/doc/277200},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Chen, Qun

AU - Jost, Jürgen

AU - Wang, Guofang

AU - Zhu, Miaomiao

TI - The boundary value problem for Dirac-harmonic maps

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 3

SP - 997

EP - 1031

AB - 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.

LA - eng

KW - Dirac-harmonic map; regularity; boundary value; Dirac-harmonic map; regularity; boundary value

UR - http://eudml.org/doc/277200

ER -

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