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MiS Preprint

The Boundary Value Problem for the Super-Liouville Equation

Jürgen Jost, Guofang Wang, Chunqin Zhou and Miaomiao Zhu


We study the boundary value problem for the -- conformally invariant -- super Liouville functional \begin{equation*} E\left( u,\psi \right) =\int_{M}\{\frac 12 \left| \nabla u\right| ^2+K_gu+\left\langle (D+e^u)\psi ,\psi \right\rangle -e^{2u}\}dz \end{equation*}} that couples a function $u$ and a spinor $\psi$ 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 $\psi$. 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.

Sep 8, 2011
Sep 9, 2011

Related publications

2014 Repository Open Access
Jürgen Jost, Guofang Wang, Chunqin Zhou and Miaomiao Zhu

The boundary value problem for the Super-Liouville equation

In: Annales de l'Institut Henri Poincaré / C, 31 (2014) 4, pp. 685-706