TY - JOUR

T1 - Note on ETH of descendant states in 2D CFT

AU - Guo, Wu zhong

AU - Lin, Feng Li

AU - Zhang, Jiaju

N1 - Funding Information:
Article funded by SCOAP3.
Publisher Copyright:
© 2019, The Author(s).

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Conformal Field Theory

KW - Gauge-gravity correspondence

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U2 - 10.1007/JHEP01(2019)152

DO - 10.1007/JHEP01(2019)152

M3 - Article

AN - SCOPUS:85060914924

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

M1 - 152

ER -