Bootstrapping Quantum Extremal Surfaces I: The Area Operator

TL;DR

This paper explores the connection between quantum extremal surfaces and the microscopic data of dual conformal field theories, focusing on AdS3/CFT2, and demonstrates how the area operator can be linked to CFT data through second-order entanglement entropy calculations.

Contribution

It systematically links quantum extremal surfaces to CFT data and computes the area operator contribution in AdS3/CFT2 at second order in large c expansion.

Findings

Virasoro identity block contributes solely to the area operator.

Second-order entanglement entropy matches the bulk area operator expectation.

Established a method to relate quantum extremal surfaces to microscopic CFT data.

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 AdS$_3$/CFT$_2$, 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.