Abstract

We study the boundary value problem for the — conformally invariant — super-Liouville functionalE(u,ψ)=∫M{12|∇u|2+Kgu+〈(D̸+eu)ψ,ψ〉−e2u}dz 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.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call