Building a Quantum Black Hole Microstate: A Bulk Path Integral for a Heavy Virasoro Primary

[2608.14541] Building a Quantum Black Hole Microstate: A Bulk Path Integral for a Heavy Virasoro Primary Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Theory arXiv:2608.14541 (hep-th) [Submitted on 14 Aug 2026] Title: Building a Quantum Black Hole Microstate: A Bulk Path Integral for a Heavy Virasoro Primary Authors: Chethan Krishnan , Rajdeep Mitra View a PDF of the paper titled Building a Quantum Black Hole Microstate: A Bulk Path Integral for a Heavy Virasoro Primary, by Chethan Krishnan and 1 other authors View PDF HTML (experimental) Abstract: Consider level-$k$ $SL(2,R) \times SL(2,R)$ Chern-Simons theory on a semi-infinite solid cylinder, with a Wilson line in the unitary principal continuous series inserted along the time direction at the center of the spatial disc. We argue that at the $\tau=0$ cut, this Euclidean path integral prepares the bulk dual of a heavy Virasoro primary above the BTZ threshold, with Drinfel'd-Sokolov (DS) reduction playing a crucial role in converting the affine module into a Virasoro module. Semi-classically, the DS constraint turns into the DS gauge, familiar from asymptotically AdS$_3$ gravity. Together with boundary gravitons, these primaries provide a bulk construction of BTZ black hole microstates at finite $k$. In the large-$k$ WKB limit, the saddle that controls an $individual$ primary is the BTZ black hole with a $singular$ horizon. We study the (grand-)canonical partition function of the microstates with density of states dictated by modular invariance. The temperature and chemical potential then fix the holonomy saddle to be the Euclidean BTZ black hole with a $smoothly$ contractible thermal cycle. A density of heavy primaries growing as $e^{2\pi\gamma QP}$ would instead lead to a defect (or excess) saddle, except at the Cardy value $\gamma=1$ fixed by modular invariance. After analytic continuation, the eternal Lorentzian black hole with a smooth horizon is therefore not just any thermal ensemble, but the ``modular ensemble" of (semi-classically singular) horizonless microstates. We compute the thermal fluctuations in this ensemble, and reproduce the fluctuations in the area of the form expected from semi-classical general relativity. Ensembles of theories do not play a direct role in any of our discussions. We also note that these microstates, unlike fuzzballs, do $not$ break the isometries of the black hole. Comments: 49+9 pages Subjects: High Energy Physics - Theory (hep-th) Cite as: arXiv:2608.14541 [hep-th] (or arXiv:2608.14541v1 [hep-th] for this version) https://doi.org/10.48550/arXiv.2608.14541 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Chethan Krishnan [ view email ] [v1] Fri, 14 Aug 2026 17:54:31 UTC (60 KB) Full-text links: Access Paper: View a PDF of the paper titled Building a Quantum Black Hole Microstate: A Bulk Path Integral for a Heavy Virasoro Primary, by Chethan Krishnan and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-08 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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