标题： 二维CFT在KdV广义系综中的全息Renyi熵 显示英文标题

标题： Holographic Renyi entropy of 2d CFT in KdV generalized ensemble

摘要： 量子混沌二维共形场论中的本征态热化假设（ETH）由于存在无限多的KdV守恒荷而变得复杂。先前的研究表明，主要共形场论本征态具有平坦的纠缠谱，这与微正则系综非常不同。这一结果明显与传统的ETH相矛盾，因为传统ETH并未考虑KdV荷。在附录论文\cite{KdVETHgeneral}中，我们通过研究混沌共形场论在KdV广义吉布斯系综和微正则系综中的子系统熵来解决这一差异。在本文中，我们在AdS/CFT的框架下进行了平行计算。我们关注高密度极限，这等价于共形理论中的热力学极限。在此极限下，全息Renyi熵可以使用所谓的粘合构造进行计算。我们具体研究了KdV广义微正则系综，其中前两个KdV荷的密度$\langle \mathcal{Q}_1\rangle = q_1,\langle \mathcal{Q}_3\rangle = q_3$被固定并遵循$q_3-q_1^2 \ll q_1^2$。 在这个区域我们发现细化Renyi熵$\tilde{S}_n$对于$n>n_{cut}$是$n$-无关的，其中$n_{cut}$依赖于$q_1,q_3$。通过取主态极限$q_3\to q_1^2$，我们恢复了固定面积态的平坦纠缠谱，这与主态行为一致。这为二维共形场论中的KdV广义ETH提供了一致性检验。 显示英文摘要

摘要： 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 $\langle \mathcal{Q}_1\rangle = q_1,\langle \mathcal{Q}_3\rangle = q_3$ 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 $q_3\to q_1^2$, 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.