Abstract
Equilibrium finite temperature observables of a CFT can be described by a local effective action for background fields — a “thermal effective action”. This effective action determines the asymptotic density of states of a CFT as a detailed function of dimension and spin. We discuss subleading perturbative and nonperturbative corrections to the density, comparing with free and holographic examples. We furthermore show how to use the thermal effective action on more complicated geometries at special locations called “hot spots”. The hot spot idea makes a prediction for a CFT partition function on a higher-dimensional version of a genus-2 Riemann surface, in a particular high temperature limit. By decomposing the partition function into a novel higher-dimensional version of genus-2 conformal blocks (which we compute at large scaling dimension), we extract the asymptotic density of heavy-heavy-heavy OPE coefficients in a higher-dimensional CFT. We also compute asymptotics of thermal 1-point functions using the same techniques.
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Acknowledgments
We thank Alex Belin, Alejandra Castro, Stuart Dowker, Liam Fitzpatrick, Tom Hartman, Zohar Komargodski, Petr Kravchuk, Alex Maloney, Henry Maxfield, Dalimil Mazáč, Jake McNamara, Shiraz Minwalla, Sridip Pal, Julio Parra-Martinez, Mukund Rangamani, Edgar Shaghoulian, Douglas Stanford, Herman Verlinde, Pedro Vieira, Yifan Wang, and Sasha Zhiboedov for helpful discussions. We thank Zohar Komargodski, Edgar Shaghoulian, and Yifan Wang for comments on the draft. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, NB is supported in part by the Sherman Fairchild Foundation. HO is supported in part by the World Premier International Research Center Initiative, MEXT, Japan, and by JSPS Grants-in-Aid for Scientific Research 20K03965 and 23K03379. DSD is supported in part by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap) and a DOE Early Career Award under grant No. DE-SC0019085.
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Benjamin, N., Lee, J., Ooguri, H. et al. Universal asymptotics for high energy CFT data. J. High Energ. Phys. 2024, 115 (2024). https://doi.org/10.1007/JHEP03(2024)115
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DOI: https://doi.org/10.1007/JHEP03(2024)115