Title: The conformal bootstrap at finite temperature

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [2];  [2]
  1. Princeton Univ., NJ (United States); Princeton Univ., NJ (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  3. Princeton Univ., NJ (United States); Inst. for Advanced Study, Princeton, NJ (United States)
+ Show Author Affiliations

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O(N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.

Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0016244
OSTI ID:
1483574
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2018; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (14)

Thermal CFTs in momentum space journal January 2020
Fast conformal bootstrap and constraints on 3d gravity journal May 2019
Easy-plane QED3’s in the large Nf limit journal May 2019
Calogero-Sutherland approach to defect blocks journal October 2018
Light-ray operators in conformal field theory journal November 2018
Recursion relation for general 3d blocks journal December 2019
Bootstrapping the long-range Ising model in three dimensions journal January 2019
Calogero-Sutherland approach to defect blocks text January 2018
Light-ray operators in conformal field theory text January 2018
Calogero-Sutherland Approach to Defect Blocks text January 2018
Bootstrapping the long-range Ising model in three dimensions text January 2018
Easy-plane QED$_3$'s in the large $N_f$ limit text January 2019
Fast Conformal Bootstrap and Constraints on 3d Gravity text January 2019
Thermal CFTs in momentum space text January 2019

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