J-holomorphic curves and Dirac-harmonic maps

Abstract

Dirac-harmonic maps are critical points of a fermionic action functional, generalizing the Dirichlet energy for harmonic maps. We consider the case where the source manifold is a closed Riemann surface with the canonical Spin c -structure determined by the complex structure and the target space is a Kähler manifold. If the underlying map f is a J-holomorphic curve, we determine the space of spinors on the Riemann surface which form Dirac-harmonic maps together with f . For suitable complex structures on the target manifold the tangent bundle to the moduli space of J-holomorphic curves consists of Diracharmonic maps.