Universal spectrum of 2d conformal field theory in the large c limit

Hartman, Thomas; Keller, Christoph A.; Stoica, Bogdan

doi:10.1007/JHEP09(2014)118

Title: Universal spectrum of 2d conformal field theory in the large c limit

Journal Article · Mon Sep 22 00:00:00 EDT 2014 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP09(2014)118· OSTI ID:1600491

Hartman, Thomas ^[1]; Keller, Christoph A. ^[2]; Stoica, Bogdan ^[3]

Univ. of California, Santa Barbara, CA (United States)
Rutgers Univ., Piscataway, NJ (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all $ \Delta \ge \frac{c}{6} $. The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States); Rutgers Univ., Piscataway, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

Grant/Contract Number:: SC0011632; SC0010008; SC0003883; SC0007897; PHY11-25915

OSTI ID:: 1600491

Journal Information:: Journal of High Energy Physics (Online), Vol. 2014, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 215 works

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