Conformal Field Theory Ground States as Critical Points of an Entropy Function

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Conformal Field Theory Ground States as Critical Points of an Entropy Function

Ting-Chun Lin (林鼎鈞) and John McGreevy

Phys. Rev. Lett. 131, 251602 – Published 21 December 2023

Abstract

We derive an entropy formula satisfied by the ground states of $1 + 1 D$ conformal field theories. The formula implies that the ground state is the critical point of an entropy function. We conjecture that this formula may serve as an information-theoretic criterion for conformal field theories, which differs from the conventional algebraic definition. In addition to these findings, we use the same proof method to extract the six global conformal generators of the conformal field theory from its ground state. We validate our results by testing them on different critical lattice models, with excellent agreement.

Received 22 June 2023
Revised 12 October 2023
Accepted 21 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.251602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society