Deep Finite Temperature Bootstrap

TL;DR

This paper introduces a new numerical bootstrap method for finite temperature conformal field theories that leverages the KMS condition, dispersion relations, and neural networks to efficiently incorporate infinite operator contributions without positivity constraints.

Contribution

The novel approach combines neural networks and thermal dispersion relations to bootstrap finite temperature CFTs without relying on positivity or truncation, expanding the toolkit for thermal bootstrap studies.

Findings

Successfully applied to Generalized Free Fields.

Performed preliminary bootstrap analysis of holographic CFTs.

Demonstrated efficiency in capturing infinite operator contributions.

Abstract

We introduce a novel method to bootstrap crossing equations in Conformal Field Theory and apply it to finite temperature theories on $S^1\times \mathbb{R}^{d-1}$. 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: $(i)$ the Kubo-Martin-Schwinger (KMS) condition, $(ii)$ thermal dispersion relations and $(iii)$ 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.