Abstract
Quantum extremal surfaces are central to the connection between quantum information theory and quantum gravity and they have played a prominent role in the recent progress on the information paradox. We initiate a program to systematically link these surfaces to the microscopic data of the dual conformal field theory, namely the scaling dimensions of local operators and their OPE coefficients. We consider CFT states obtained by acting on the vacuum with single-trace operators, which are dual to one-particle states of the bulk theory. Focusing on AdS3/CFT2, we compute the CFT entanglement entropy to second order in the large c expansion where quantum extremality becomes important and match it to the expectation value of the bulk area operator. We show that to this order, the Virasoro identity block contributes solely to the area operator.
Highlights
A the boundary CFT semi-classically in the bulk from the generalized entropy of a special surface [1,2,3,4,5,6]
The term SEbuElk(ΣA) refers to the entanglement entropy associated to the codimension-1 region RA bounded by ΣA and A, for all quantum fields that propagate on a given background
This paper is the first in a series of papers aimed at constructing a dictionary between CFT OPE data given by the conformal dimensions and OPE coefficients of single- and double-trace operators, and the contributions to the expectation value of the area operator and the bulk entanglement entropy appearing in the generalized entropy
Summary
This paper is the first in a series of papers aimed at constructing a dictionary between CFT OPE data given by the conformal dimensions and OPE coefficients of single- and double-trace operators, and the contributions to the expectation value of the area operator and the bulk entanglement entropy appearing in the generalized entropy. To obtain the entanglement entropy, one needs to perform an analytic continuation in the Rényi index n, which can be achieved term by term in an OPE expansion This framework provides a bridge between the microscopic CFT data in a large c expansion and quantum extremal surfaces in the bulk. Be responsible for deviations of the low-energy EFT from semi-classical general relativity minimally coupled to matter Such effects would appear as corrections in any top-down model whose bulk dual is given by string theory in AdS. This part of the dictionary would be interesting to construct as it would give α corrections to the quantum HRRT formula (1.1), and could probe entanglement in string theory beyond higher derivative corrections to entanglement entropy [42, 43]. By matching the various contributions on the two sides of the quantum HRRT formula (1.1), we will eventually obtain an explicit check of this formula which, to our knowledge, has not been done in the literature far ( see [44] for an explicit check in a doubly holographic setup)
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