Modular Commutators in Conformal Field Theory

• URL: http://arxiv.org/abs/2206.00027v3
• Date: Tue, 14 Jun 2022 07:34:52 GMT
• Title: Modular Commutators in Conformal Field Theory
• Authors: Yijian Zou, Bowen Shi, Jonathan Sorce, Ian T. Lim, and Isaac H. Kim
• Abstract summary: We show that the modular commutator depends only on the chiral central charge and the conformal cross ratio. We propose a geometric dual for the modular commutator in certain preferred states of the AdS/CFT correspondence.
• Score: 5.02033914945157
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The modular commutator is a recently discovered multipartite entanglement measure that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in conformal field theories in $1+1$ dimensions and discuss its salient features. We show that the modular commutator depends only on the chiral central charge and the conformal cross ratio. We test this formula for a gapped $(2+1)$-dimensional system with a chiral edge, i.e., the quantum Hall state, and observe excellent agreement with numerical simulations. Furthermore, we propose a geometric dual for the modular commutator in certain preferred states of the AdS/CFT correspondence. For these states, we argue that the modular commutator can be obtained from a set of crossing angles between intersecting Ryu-Takayanagi surfaces.

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