Note on ETH of descendant states in 2D CFT

Wu zhong Guo, Feng Li Lin, Jiaju Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We investigate the eigenstate thermalization hypothesis (ETH) of highly excited descendant states in two-dimensional large central charge c conformal field theory. We use operator product expansion of twist operators to calculate the short interval expansions of entanglement entropy and relative entropy for an interval of length ℓ up to order ℓ12. Using these results to ensure ETH of a heavy state when compared with the canonical ensemble state up to various orders of c, we get the constraints on the expectation values of the first few quasiprimary operators in the vacuum conformal family at the corresponding order of c. Similarly, we also obtain the constraints from the expectation values of the first few Korteweg-de Vries charges. We check these constraints for some types of special descendant excited states. Among the descendant states we consider, we find that at most only the leading order ones of the ETH constraints can be satisfied for the descendant states that are slightly excited on top of a heavy primary state. Otherwise, the ETH constraints are violated for the descendant states that are heavily excited on top of a primary state.

Original languageEnglish
Article number152
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 2019 Jan 1


  • AdS-CFT Correspondence
  • Conformal Field Theory
  • Gauge-gravity correspondence

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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