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Deep finite temperature bootstrap

V. Niarchos1,*, C. Papageorgakis2,†, A. Stratoudakis1,‡, and M. Woolley2,§

  • *Contact author: niarchos@physics.uoc.gr
  • †Contact author: c.papageorgakis@qmul.ac.uk
  • ‡Contact author: astratoudakis@physics.uoc.gr
  • §Contact author: mitchell.woolley@qmul.ac.uk
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Phys. Rev. D 112, 126012 – Published 16 December, 2025

DOI: https://doi.org/10.1103/qrjx-w4md

Abstract

We introduce a novel method to bootstrap crossing equations in conformal field theory (CFT) and apply it to finite temperature theories on S1×Rd−1. The proposed approach does not rely on positivity constraints and does not employ uncontrolled truncation schemes. Instead, we capture the contribution of an infinite number of operators in conformal block expansions using suitable functions, which are bootstrapped (numerically) together with a finite number of exposed CFT data. Our approach at finite temperature employs three key ingredients: (1) the Kubo-Martin-Schwinger (KMS) condition, (2) thermal dispersion relations, and (3) neural networks that model spin-dependent tail functions within the conformal block expansions. We test the efficiency of the new method in the case of generalized free fields and use it to perform a preliminary bootstrap analysis of double-twist thermal data in holographic CFTs.

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Phys. Rev. D 112, 126012– Published 16 December, 2025
  • Received 6 September 2025
  • Accepted 26 November 2025
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