The Conformal Bootstrap at Finite Temperature
read the original abstract
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.
This paper has not been read by Pith yet.
Forward citations
Cited by 11 Pith papers
-
Neural Spectral Bias and Conformal Correlators I: Introduction and Applications
Neural networks optimized solely on crossing symmetry reconstruct CFT correlators from minimal input data to few-percent accuracy across generalized free fields, minimal models, Ising, N=4 SYM, and AdS diagrams.
-
Crosscap Defects
Crosscap defects are introduced in CFTs via Z2 quotients, with crossing equations derived and CFT data computed in the O(N) model at Gaussian and Wilson-Fisher points showing absent displacement and tilt operators for...
-
Crosscap Defects
Crosscap defects from Z2 spacetime quotients in CFTs yield new crossing equations and O(N) model examples without displacement or tilt operators, forming defect conformal manifolds lacking exactly marginal operators.
-
$\mathcal{PT}$-symmetric Field Theories at Finite Temperature
A thermal normal-ordering scheme yields systematic epsilon-expansions for thermal observables in PT-symmetric cubic and quintic O(N) models, agreeing with exact 2D results from minimal models M(2,5) and M(3,8)_D and p...
-
Efficient Conformal Block Evaluation with GoBlocks
GoBlocks delivers faster recursive evaluation of conformal blocks than prior packages, enabling mixed-correlator bootstrap optimizations for the 3D Ising model and O(N) vectors.
-
Strongly Coupled Sectors in Inflation: Gapped Theories of Unparticles
Compactified 5D unparticle theories generate gapped excitations whose exchange in inflationary correlators yields oscillations modulated by anomalous dimensions and possible interference patterns under brane-localized...
-
The analytic bootstrap at finite temperature
Universal dispersion-based formulae for thermal two-point functions of scalars that satisfy bootstrap axioms except clustering at infinite distance.
-
Neural Networks Reveal a Universal Bias in Conformal Correlators
Neural networks trained on crossing symmetry accurately reconstruct conformal correlators from minimal inputs due to alignment between their spectral bias and CFT smoothness.
-
Bouncing singularities and thermal correlators on line defects
Retarded correlators of displacement operators on line defects in holographic thermal CFTs exhibit bouncing singularities that match between interior-sensitive WKB and boundary-only OPE analyses.
-
Imprint of the black hole singularity on thermal two-point functions
Thermal two-point functions in holographic AdS black holes receive exponentially small non-perturbative corrections controlled by null geodesics bouncing off the singularity.
-
Neural Networks, Dispersion Relations and the Thermal Bootstrap
A neural-network approach with dispersion relations handles infinite OPE towers in thermal conformal correlators without positivity.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.