Remarks on entanglement entropy for gauge fields

Horacio Casini, Marina Huerta, and José Alejandro Rosabal
Phys. Rev. D 89, 085012 – Published 7 April 2014

Abstract

In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due to the presence of a center—a set of operators which commute with all others—in the gauge invariant operator algebra corresponding to a finite region. A unique entropy can be assigned to algebras with a center, giving a place to a local entropy in lattice gauge theories. However, ambiguities arise on the correspondence between algebras and regions. In particular, it is always possible to choose (in many different ways) local algebras with a trivial center, and hence a genuine entanglement entropy, for any region. These choices are in correspondence with maximal trees of links on the boundary, which can be interpreted as partial gauge fixings. This interpretation entails a gauge fixing dependence of the entanglement entropy. In the continuum limit, however, ambiguities in the entropy are given by terms local on the boundary of the region, in such a way relative entropy and mutual information are finite, universal, and gauge independent quantities.

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  • Received 30 January 2014

DOI:https://doi.org/10.1103/PhysRevD.89.085012

© 2014 American Physical Society

Authors & Affiliations

Horacio Casini*, Marina Huerta, and José Alejandro Rosabal

  • Centro Atómico Bariloche, 8400-S.C. de Bariloche, Río Negro, Argentina

  • *casini@cab.cnea.gov.ar
  • marina.huerta@cab.cnea.gov.ar
  • alejo_rosabal@yahoo.es

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Issue

Vol. 89, Iss. 8 — 15 April 2014

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