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.
Dynamics of Finite-Temperature Conformal Field Theories from Operator Product Expansion Inversion Formulas
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abstract
We apply the OPE inversion formula to thermal two-point functions of bosonic and fermionic CFTs in general odd dimensions. This allows us to analyze in detail the operator spectrum of these theories. We find that nontrivial thermal CFTs arise when the thermal mass satisfies an algebraic transcendental equation that ensures the absence of an infinite set of operators from the spectrum. The solutions of these gap equations for general odd dimensions are in general complex numbers and follow a particular pattern. We argue that this pattern unveils the large-$N$ vacuum structure of the corresponding theories at zero temperature.
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hep-th 5representative citing papers
Universal dispersion-based formulae for thermal two-point functions of scalars that satisfy bootstrap axioms except clustering at infinite distance.
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 providing higher-d extrapolations.
Neural networks trained on crossing symmetry accurately reconstruct conformal correlators from minimal inputs due to alignment between their spectral bias and CFT smoothness.
A neural-network approach with dispersion relations handles infinite OPE towers in thermal conformal correlators without positivity.
citing papers explorer
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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.
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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.
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$\mathcal{PT}$-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 providing higher-d extrapolations.
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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.
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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.