The Boundary Value Problem for the Super-Liouville Equation

Jürgen Jost, Guofang Wang, Chunqin Zhou, and Miaomiao Zhu

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Submission date: 08. Sep. 2011
Pages: 24
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Abstract:
>We study the boundary value problem for the – conformally invariant – super Liouville functional

that couples a function u and a spinor ψ on a Riemann surface. The boundary condition that we identify (motivated by quantum field theory) couples a Neumann condition for u with a chirality condition for ψ. Associated to any solution of the super Liouville system is a holomorphic quadratic differential T(z), and when our boundary condition is satisfied, T becomes real on the boundary.
We provide a complete regularity and blow-up analysis for solutions of this boundary value problem.