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

Anatoly Dymarsky, Kirill Pavlenko, Dmitry Solovyev

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2 Scopus citations


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.

Original languageEnglish
Article number172
JournalJournal of High Energy Physics
Issue number7
StatePublished - Jul 1 2020

Bibliographical note

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).


  • Conformal Field Theory
  • Conformal and W Symmetry
  • Integrable Field The- ories

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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