One-loop effect in the charged 2D black hole near extremality

Abstract

We study the one-loop correction to the near-extremal quantum entropy of the charged two-dimensional black hole introduced in \cite{McGuigan:1992}. In target space this background can be understood as arising from the dimensional reduction of a three-dimensional solution of the low-energy string effective action. On the other hand, its worldsheet description is provided by the dimensionally reduced $\frac{SL(2,\mathbb{R})\times U(1)}{U(1)}$ WZW model. Using this latter formulation, we compute the torus partition function to extract the temperature dependence of the one-loop stringy correction to the quantum entropy arising from the short-string sector. We show that this result is under control as long as the black hole temperature satisfies the condition $T\gtrsim \frac{1}{4\pi \sqrt{k}}$, where the saturation of this bound corresponds to the long-string contribution to the free energy becoming divergent. We speculate that this threshold behavior of the partition function can be interpreted as a signature of the black hole/string transition.

23 pages, 4 appendices. Final version

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