TY - JOUR

T1 - Zero modes of local operators in 2d CFT on a cylinder

AU - Dymarsky, Anatoly

AU - Pavlenko, Kirill

AU - Solovyev, Dmitry

N1 - Funding Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited Publisher Copyright: © 2020, The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/7/23

Y1 - 2020/7/23

N2 - Studies of Eigenstate Thermalization Hypothesis (ETH) in two-dimensional CFTs call for calculation of the expectation values of local operators in highly excited energy eigenstates. This can be done efficiently by representing zero modes of these operators in terms of the Virasoro algebra generators. In this paper we present a pedagogical introduction explaining how this calculation can be performed analytically or using computer algebra. We illustrate the computation of zero modes by a number of examples and list explicit expressions for all local operators from the vacuum family with the dimension of less or equal than eight. Finally, we derive an explicit expression for the quantum KdV generator Q7 in terms of the Virasoro algebra generators. The obtained results can be used for quantitative studies of ETH at finite value of central charge.

AB - Studies of Eigenstate Thermalization Hypothesis (ETH) in two-dimensional CFTs call for calculation of the expectation values of local operators in highly excited energy eigenstates. This can be done efficiently by representing zero modes of these operators in terms of the Virasoro algebra generators. In this paper we present a pedagogical introduction explaining how this calculation can be performed analytically or using computer algebra. We illustrate the computation of zero modes by a number of examples and list explicit expressions for all local operators from the vacuum family with the dimension of less or equal than eight. Finally, we derive an explicit expression for the quantum KdV generator Q7 in terms of the Virasoro algebra generators. The obtained results can be used for quantitative studies of ETH at finite value of central charge.

KW - Conformal and W Symmetry

KW - Conformal Field Theory

KW - Integrable Field The- ories

KW - STATISTICAL-MECHANICS

KW - CHAOS

KW - CONFORMAL FIELD-THEORY

KW - THERMALIZATION

KW - QUANTUM

KW - INTEGRABLE STRUCTURE

UR - http://www.scopus.com/inward/record.url?scp=85088468907&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2020)172

DO - 10.1007/JHEP07(2020)172

M3 - Article

AN - SCOPUS:85088468907

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 172

ER -