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Journal of High Energy Physics

, 2018:29 | Cite as

Lorentz-diffeomorphism edge modes in 3d gravity

  • Marc Geiller
Open Access
Regular Article - Theoretical Physics

Abstract

The proper definition of subsystems in gauge theory and gravity requires an extension of the local phase space by including edge mode fields. Their role is on the one hand to restore gauge invariance with respect to gauge transformations supported on the boundary, and on the other hand to parametrize the largest set of boundary symmetries which can arise if both the gauge parameters and the dynamical fields are unconstrained at the boundary. In this work we construct the extended phase space for three-dimensional gravity in first order connection and triad variables. There, the edge mode fields consist of a choice of coordinate frame on the boundary and a choice of Lorentz frame on the bundle, which together constitute the Lorentz-diffeomorphism edge modes. After constructing the extended symplectic structure and proving its gauge invariance, we study the boundary symmetries and the integrability of their generators. We find that the infinite-dimensional algebra of boundary symmetries with first order variables is the same as that with metric variables, and explain how this can be traced back to the expressions for the diffeomorphism Noether charge in both formulations. This concludes the study of extended phase spaces and edge modes in three-dimensional gravity, which was done previously by the author in the BF and Chern-Simons formulations.

Keywords

Classical Theories of Gravity Gauge Symmetry Global Symmetries 

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) 2018

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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