Holographic Renyi entropy of 2d CFT in KdV generalized ensemble

Kavli Affiliate: Huajia Wang

| First 5 Authors: Liangyu Chen, Anatoly Dymarsky, Jia Tian, Huajia Wang,

| Summary:

The eigenstate thermalization hypothesis (ETH) in chaotic two dimensional
CFTs is subtle due to infinitely many conserved KdV charges. Previous works
have demonstrated that primary CFT eigenstates have flat entanglement spectrum,
which is very different from the microcanonical ensemble. This result is an
apparent contradiction to conventional ETH, which does not take KdV charges
into account. In a companion paper cite{KdVETHgeneral}, we resolve this
discrepancy by studying the subsystem entropy of a chaotic CFT in
KdV-generalized Gibbs and microcanonical ensembles. In this paper, we carry out
parallel computations in the context of AdS/CFT. We focus on the high density
limit, which is equivalent to thermodynamic limit in conformal theories. In
this limit holographic Renyi entropy can be computed using the so-called gluing
construction. We explicitly study the KdV-generalized microcanonical ensemble
with the densities of the first two KdV charges $langle mathcal{Q}_1rangle =
q_1,langle mathcal{Q}_3rangle = q_3$ fixed and obeying $q_3-q_1^2 ll
q_1^2$. In this regime we found that the refined Renyi entropy $tilde{S}_n$ is
$n$-independent for $n>n_{cut}$, where $n_{cut}$ depends on $q_1,q_3$. By
taking the primary state limit $q_3to q_1^2$, we recover flat entanglement
spectrum characteristic of fixed-area states, in agreement with the primary
state behavior. This provides a consistency check of the KdV-generalized ETH in
2d CFTs.

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