Regularity of Dirac-harmonic maps with λ−curvature term in higher dimensions
Jürgen Jost, Lei Liu, and Miaomiao Zhu
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Submission date: 27. Mar. 2017 (revised version: April 2017)
published in: Calculus of variations and partial differential equations, 58 (2019) 6, art-no. 187
DOI number (of the published article): 10.1007/s00526-019-1632-y
Keywords and phrases: Supersymmetric nonlinear sigma model, Dirac-harmonic maps with $\lambda-$curvature term, Monotonicity formula, partial regularity
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In this paper, we will study the partial regularity for stationary Dirac-harmonic maps with λ−curvature term. For a weakly stationary Dirac-harmonic map with λ−curvature term (ϕ,ψ) from a smooth bounded open domain Ω ⊂ ℝm with m ≥ 2 to a compact Riemannian manifold N, if ψ ∈ W1,p(Ω) for some p >, we prove that (ϕ,ψ) is smooth outside a closed singular set whose (m − 2)-dimensional Hausdorff measure is zero. Furthermore, if the target manifold N does not admit any harmonic sphere Sl, l = 2,...,m − 1, then (ϕ,ψ) is smooth.