Exact Bosonic and Supersymmetric String Black Hole Solutions
  We show that Witten's two-dimensional string black hole metric is exactly conformally invariant in the supersymmetric case. We also demonstrate that this metric, together with a recently proposed exact metric for the bosonic case, are respectively consistent with the supersymmetric and bosonic $\sigma$-model conformal invariance conditions up to four-loop order. 
I. Jack, D. R. T. Jones and J. Panvel