Extended actions, dynamics of edge modes, and entanglement entropy
Abstract In this work we propose a simple and systematic framework for including edge modes in gauge theories on manifolds with boundaries. We argue that this is necessary in order to achieve the factorizability of the path integral, the Hilbert space and the phase space, and that it explains how ed...
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doaj-c4908e2731044920877ad30691e3654e2020-11-25T03:13:17ZengSpringerOpenJournal of High Energy Physics1029-84792020-09-012020915710.1007/JHEP09(2020)134Extended actions, dynamics of edge modes, and entanglement entropyMarc Geiller0Puttarak Jai-akson1Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, UMR 5672Perimeter Institute for Theoretical PhysicsAbstract In this work we propose a simple and systematic framework for including edge modes in gauge theories on manifolds with boundaries. We argue that this is necessary in order to achieve the factorizability of the path integral, the Hilbert space and the phase space, and that it explains how edge modes acquire a boundary dynamics and can contribute to observables such as the entanglement entropy. Our construction starts with a boundary action containing edge modes. In the case of Maxwell theory for example this is equivalent to coupling the gauge field to boundary sources in order to be able to factorize the theory between subregions. We then introduce a new variational principle which produces a systematic boundary contribution to the symplectic structure, and thereby provides a covariant realization of the extended phase space constructions which have appeared previously in the literature. When considering the path integral for the extended bulk + boundary action, integrating out the bulk degrees of freedom with chosen boundary conditions produces a residual boundary dynamics for the edge modes, in agreement with recent observations concerning the contribution of edge modes to the entanglement entropy. We put our proposal to the test with the familiar examples of Chern-Simons and BF theory, and show that it leads to consistent results. This therefore leads us to conjecture that this mechanism is generically true for any gauge theory, which can therefore all be expected to posses a boundary dynamics. We expect to be able to eventually apply this formalism to gravitational theories.http://link.springer.com/article/10.1007/JHEP09(2020)134Gauge SymmetryChern-Simons Theories |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Marc Geiller Puttarak Jai-akson |
spellingShingle |
Marc Geiller Puttarak Jai-akson Extended actions, dynamics of edge modes, and entanglement entropy Journal of High Energy Physics Gauge Symmetry Chern-Simons Theories |
author_facet |
Marc Geiller Puttarak Jai-akson |
author_sort |
Marc Geiller |
title |
Extended actions, dynamics of edge modes, and entanglement entropy |
title_short |
Extended actions, dynamics of edge modes, and entanglement entropy |
title_full |
Extended actions, dynamics of edge modes, and entanglement entropy |
title_fullStr |
Extended actions, dynamics of edge modes, and entanglement entropy |
title_full_unstemmed |
Extended actions, dynamics of edge modes, and entanglement entropy |
title_sort |
extended actions, dynamics of edge modes, and entanglement entropy |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-09-01 |
description |
Abstract In this work we propose a simple and systematic framework for including edge modes in gauge theories on manifolds with boundaries. We argue that this is necessary in order to achieve the factorizability of the path integral, the Hilbert space and the phase space, and that it explains how edge modes acquire a boundary dynamics and can contribute to observables such as the entanglement entropy. Our construction starts with a boundary action containing edge modes. In the case of Maxwell theory for example this is equivalent to coupling the gauge field to boundary sources in order to be able to factorize the theory between subregions. We then introduce a new variational principle which produces a systematic boundary contribution to the symplectic structure, and thereby provides a covariant realization of the extended phase space constructions which have appeared previously in the literature. When considering the path integral for the extended bulk + boundary action, integrating out the bulk degrees of freedom with chosen boundary conditions produces a residual boundary dynamics for the edge modes, in agreement with recent observations concerning the contribution of edge modes to the entanglement entropy. We put our proposal to the test with the familiar examples of Chern-Simons and BF theory, and show that it leads to consistent results. This therefore leads us to conjecture that this mechanism is generically true for any gauge theory, which can therefore all be expected to posses a boundary dynamics. We expect to be able to eventually apply this formalism to gravitational theories. |
topic |
Gauge Symmetry Chern-Simons Theories |
url |
http://link.springer.com/article/10.1007/JHEP09(2020)134 |
work_keys_str_mv |
AT marcgeiller extendedactionsdynamicsofedgemodesandentanglemententropy AT puttarakjaiakson extendedactionsdynamicsofedgemodesandentanglemententropy |
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