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 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 language | English |
|---|---|
| Article number | 152 |
| Journal | Journal of High Energy Physics |
| Volume | 2019 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 Jan 1 |
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Keywords
- AdS-CFT Correspondence
- Conformal Field Theory
- Gauge-gravity correspondence
ASJC Scopus subject areas
- Nuclear and High Energy Physics
Cite this
Note on ETH of descendant states in 2D CFT. / Guo, Wu zhong; Lin, Feng Li; Zhang, Jiaju.
In: Journal of High Energy Physics, Vol. 2019, No. 1, 152, 01.01.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Note on ETH of descendant states in 2D CFT
AU - Guo, Wu zhong
AU - Lin, Feng Li
AU - Zhang, Jiaju
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
UR - http://www.scopus.com/inward/record.url?scp=85060914924&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060914924&partnerID=8YFLogxK
U2 - 10.1007/JHEP01(2019)152
DO - 10.1007/JHEP01(2019)152
M3 - Article
VL - 2019
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 1
M1 - 152
ER -