Regularity Theorems and Energy Identities for Dirac-Harmonic Maps

Details Regularity Theorems and Energy Identities for Dirac-Harmonic Maps Regularity Theorems and Energy Identities for Dirac-Harmonic Maps

2004-11-15

arxiv.org/abs/math/0411327v1

Mathematics

Differential Geometry

to appear in Math.Zeitschrift

Scientific paper

We study a new set of coupled field equations motivated by the non-linear supersymmetric sigma model of quantum field theory. These equations couple a map into a Riemannian manifold controlled by a harmonic map like action with a spinor field along that map. We study the solutions which we call Dirac-harmonic maps from a Riemann surface to a sphere $\S^n$. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.

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