Super-Liouville Equations on Closed Riemann Surfaces
  Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler-Lagrange equations, culminating in a blow up analysis. 
Juergen Jost, Guofang Wang, Chunqin Zhou