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

[摘要] We study the one-loop correction to the near-extremal quantum entropy of the charged two-dimensional black hole introduced in [1]. 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 SL2ℝ×U1U1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \frac{\mathrm{SL}\left(2,\mathbb{R}\right)\times \mathrm{U}(1)}{\mathrm{U}(1)} $$\end{document} 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≳14πk\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ T\gtrsim \frac{1}{4\pi \sqrt{k}} $$\end{document}, 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.

[发布日期] 2026-09-03

[关键词] Black Holes in String Theory;Bosonic Strings;Sigma Models