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Regularity Theorems and Energy Identities for Dirac-Harmonic Maps

Qun Chen·Juergen Jost·Guofang Wang·Jiayu Li
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Abstract

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 $§^n$. 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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Qun Chen, Juergen Jost, Guofang Wang, Jiayu Li. 2004-11-15. Regularity Theorems and Energy Identities for Dirac-Harmonic Maps. https://arxiv.org/abs/math/0411327

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