Entanglement Asymmetry in Conformal Field Theory and Holography

Francesco Benini; Victor Godet; Amartya Harsh Singh

doi:10.1093/ptep/ptaf080

journal article Open Access May 21, 2025

Entanglement Asymmetry in Conformal Field Theory and Holography

Francesco Benini

Victor Godet

Amartya Harsh Singh

Progress of Theoretical and Experimental Physics Vol. 2025 No. 6 · Oxford University Press (OUP)

View at Publisher Save 10.1093/ptep/ptaf080

Abstract

Abstract
Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems, inspired by quantum information theory, particularly suited to study out-of-equilibrium states. We study the entanglement asymmetry of a class of excited “coherent states” in conformal quantum field theories with a U(1) symmetry, employing Euclidean path-integral methods with topological symmetry defects and the replica formalism. We compute, at leading order in perturbation theory, the asymmetry for a variety of subsystems, including finite spherical subregions in flat space, in finite volume, and at positive temperature. We also study its Lorentzian time evolution, showcasing the dynamical restoration of the symmetry due to thermalization, as well as the presence of a quantum Mpemba effect. Our results are universal, and apply in any number of dimensions. We also show that the perturbative entanglement asymmetry is related to the Fisher information metric, which has a known holographic dual called the Hollands–Wald canonical energy, and that it is captured by the anti-de-Sitter bulk charge contained in the entanglement wedge.

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Published: May 21, 2025
Vol/Issue: 2025(6)
License: View

Authors

F

Francesco Benini

SISSA , Via Bonomea 265, 34136 Trieste, https://ror.org/004fze387 ,; INFN, Sezione di Trieste , Via Valerio 2, 34127 Trieste ,; ICTP, Strada Costiera 11 , 34151 Trieste ,

V

Victor Godet

SISSA , Via Bonomea 265, 34136 Trieste, https://ror.org/004fze387 ,; INFN, Sezione di Trieste , Via Valerio 2, 34127 Trieste ,

A

Amartya Harsh Singh

SISSA , Via Bonomea 265, 34136 Trieste, https://ror.org/004fze387 ,; INFN, Sezione di Trieste , Via Valerio 2, 34127 Trieste ,

Funding

SCOAP

Cite This Article

Francesco Benini, Victor Godet, Amartya Harsh Singh (2025). Entanglement Asymmetry in Conformal Field Theory and Holography. Progress of Theoretical and Experimental Physics, 2025(6). https://doi.org/10.1093/ptep/ptaf080

Entanglement Asymmetry in Conformal Field Theory and Holography

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