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Entanglement entropy, relative entropy and duality

  • Upamanyu MoitraEmail author
  • Ronak M Soni
  • Sandip P. Trivedi
Open Access
Regular Article - Theoretical Physics

Abstract

A definition for the entanglement entropy in both Abelian and non-Abelian gauge theories has been given in the literature, based on an extended Hilbert space construction. The result can be expressed as a sum of two terms, a classical term and a quantum term. It has been argued that only the quantum term is extractable through the processes of quantum distillation and dilution. Here we consider gauge theories in the continuum limit and argue that quite generically, the classical piece is dominated by modes with very high momentum, of order the cut-off, in the direction normal to the entangling surface. As a result, we find that the classical term does not contribute to the relative entropy or the mutual information, in the continuum limit, for states which only carry a finite amount of energy above the ground state. We extend these considerations for p-form theories, and also discuss some aspects pertaining to electric-magnetic duality.

Keywords

Duality in Gauge Field Theories Field Theories in Higher Dimensions Field Theories in Lower Dimensions Lattice Quantum Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia
  2. 2.Stanford Institute of Theoretical PhysicsStanford UniversityStanfordU.S.A.

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