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Journal of High Energy Physics

, 2019:152 | Cite as

Note on ETH of descendant states in 2D CFT

  • Wu-zhong Guo
  • Feng-Li Lin
  • Jiaju ZhangEmail author
Open Access
Regular Article - Theoretical Physics
  • 62 Downloads

Abstract

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 12. 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.

Keywords

AdS-CFT Correspondence Conformal Field Theory Gauge-gravity correspondence 

Notes

Open Access

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.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Physics Division, National Center for Theoretical SciencesNational Tsing Hua UniversityHsinchuTaiwan
  2. 2.Department of PhysicsNational Taiwan Normal UniversityTaipeiTaiwan
  3. 3.Dipartimento di Fisica G. OcchialiniUniversità degli Studi di Milano-BicoccaMilanoItaly
  4. 4.SISSA and INFNTriesteItaly

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