Some aspects of Dirac-harmonic maps with curvature term

Abstract

Abstract. We study several geometric and analytic aspects of Dirac-harmonic maps with curvature term from closed Riemannian surfaces.

Coarse regularity of solutions to a nonlinear sigma-model with $$L^p$$ L p gravitino

“…We can now turn to the regularity of the critical points of the action functional (1), or equivalently the solutions of the Euler-Lagrange equations (2) and (3). In contrast to Theorem 1.1, the solutions of the Euler-Lagrange equations have the expected regularities, due to the structure of the equations.…”

“…[22][23][24][25] enable us to utilize the antisymmetric structure of the equations for φ to improve the regularity. Using similar methods, regularity results for weak solutions of the simpler models, namely Dirac-harmonic maps and Dirac-harmonic maps with curvature terms, are achieved in [3,9,27,28]. Here in this more general model, the structure of the system is even more complicated because of the divergence terms and the appearance of the gravitinos.…”

“…[26] in dimension m ≥ 2 and see e.g. [3,25] in dimension m = 2. The above result improves that in Lemma 6.1 in [19], where the case of s = 2 was done and we include the sketch of the proof here only for the convenience of readers.…”

“…Note that in the particular case where the gravitino vanishes, this reduces to the Dirac-harmonic map functional with curvature term introduced in [8] and further studied in e.g. [3,4,18]. If in addition, the curvature terms in the Lagrangian also vanish, this reduces to the Dirac-harmonic map functional introduced in [6,7], which is studied to a great extent in e.g.…”

“…For the cases of the simpler models, namely Dirac-harmonic maps and Dirac-harmonic maps with curvature terms, see [3,9,18,25,28].…”