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<p><i>α</i><sup>′</sup> corrections to near horizon dynamics of a Schwarzschild black hole in a large number of spacetime dimensions <i>D</i> are governed by the worldsheet theory composed of the cigar CFT and the classical sigma model on the sphere at the horizon, along with a timelike-Liouville theory of central charge 26 – <i>D</i>. At leading order in weak string coupling, black hole thermodynamics is insensitive to the details of timelike Liouville theory. In this limit, we use the Lewkowycz-Maldacena-trick motivated infinitesimally off-shell closed string worldsheet formalism in [arxiv: 2310.02313] to calculate thermal entropy exactly in <i>α</i><sup>′</sup>. The leading term in the <i>α</i><sup>′</sup> → 0 limit and the first stingy correction of our result are in precise agreement with the target space Callan-Myers-Perry formula. Also, we point out a remarkable simplification at an ultra-low temperature of order <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mn>1</mn> <mo>/</mo> <msqrt> <mrow> <msup> <mi>α</mi> <mo>′</mo> </msup> <mi>D</mi> </mrow> </msqrt> </math></EquationSource> <EquationSource Format="TEX">\( 1/\sqrt{\alpha^{\prime }D} \)</EquationSource> </InlineEquation> and show that for a certain special set of vertex operators involving modes of the <i>D</i> dimensional spacetime and the time-like Liouville theory, the resulting worldsheet theory is related to Virasoro minimal string.</p>

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Stretched horizon, replica trick and off-shell winding condensate, and all that

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  • 发表日期：

    2025年7月16日

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  • Indranil Halder,
  • Daniel L. Jafferis

摘要

α′ corrections to near horizon dynamics of a Schwarzschild black hole in a large number of spacetime dimensions D are governed by the worldsheet theory composed of the cigar CFT and the classical sigma model on the sphere at the horizon, along with a timelike-Liouville theory of central charge 26 – D. At leading order in weak string coupling, black hole thermodynamics is insensitive to the details of timelike Liouville theory. In this limit, we use the Lewkowycz-Maldacena-trick motivated infinitesimally off-shell closed string worldsheet formalism in [arxiv: 2310.02313] to calculate thermal entropy exactly in α′. The leading term in the α′ → 0 limit and the first stingy correction of our result are in precise agreement with the target space Callan-Myers-Perry formula. Also, we point out a remarkable simplification at an ultra-low temperature of order 1 / α ′ D \( 1/\sqrt{\alpha^{\prime }D} \) and show that for a certain special set of vertex operators involving modes of the D dimensional spacetime and the time-like Liouville theory, the resulting worldsheet theory is related to Virasoro minimal string.