## Video URL

http://pirsa.org/22100092# Modular commutators in conformal field theory, topological order, and holography

### APA

Zou, Y. (2022). Modular commutators in conformal field theory, topological order, and holography. Perimeter Institute for Theoretical Physics. http://pirsa.org/22100092

### MLA

Zou, Yijian. Modular commutators in conformal field theory, topological order, and holography. Perimeter Institute for Theoretical Physics, Oct. 11, 2022, http://pirsa.org/22100092

### BibTex

@misc{ scitalks_PIRSA:22100092, doi = {}, url = {http://pirsa.org/22100092}, author = {Zou, Yijian}, keywords = {Quantum Matter}, language = {en}, title = {Modular commutators in conformal field theory, topological order, and holography}, publisher = {Perimeter Institute for Theoretical Physics}, year = {2022}, month = {oct}, note = {PIRSA:22100092 see, \url{https://scitalks.ca/PIRSA/22100092}} }

Yijian Zou Perimeter Institute for Theoretical Physics

## 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.

Zoom link: https://pitp.zoom.us/j/94069836709?pwd=RlA2ZUsxdXlPTlh2TStObHFDNUY0Zz09