Note on ETH of descendant states in 2D CFT

Guo, Wu-zhong (0000 0004 0532 0580, Physics Division, National Center for Theoretical Sciences, National Tsing Hua University, No. 101, Sec. 2, Kuang Fu Road, Hsinchu, 30013, Taiwan) ; Lin, Feng-Li (0000 0001 2158 7670, Department of Physics, National Taiwan Normal University, No. 88, Sec. 4, Ting-Chou Road, Taipei, 11677, Taiwan) ; Zhang, Jiaju (0000 0001 2174 1754, Dipartimento di Fisica G. Occhialini, Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126, Milano, Italy) (0000 0004 1762 9868, SISSA and INFN, via Bonomea 265, 34136, Trieste, Italy)

19 January 2019

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 ℓ 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.

Published in: JHEP 1901 (2019) 152
Published by: Springer/SISSA
DOI: 10.1007/JHEP01(2019)152
arXiv: 1810.01258
License: CC-BY-4.0

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