Exact Bosonic and Supersymmetric String Black Hole Solutions

TL;DR

This paper demonstrates that certain two-dimensional string black hole solutions are exactly conformally invariant in both bosonic and supersymmetric cases, consistent with higher-loop order $\sigma$-model conditions.

Contribution

It provides exact conformal invariance proofs for Witten's 2D black hole metrics in both bosonic and supersymmetric string theories.

Findings

Supersymmetric black hole metric is exactly conformally invariant.

Bosonic black hole metric is consistent with four-loop $\sigma$-model conformal invariance.

Both metrics satisfy conformal invariance conditions up to four-loop order.

Abstract

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.