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Deformed Heisenberg charges in three-dimensional gravity

Namburi, JC and Wieland, W (2020) Deformed Heisenberg charges in three-dimensional gravity. In: Journal of High Energy Physics, 2020 (3).

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Official URL: https://dx.doi.org/10.1007/JHEP03(2020)175


We consider the bulk plus boundary phase space for three-dimensional gravity with negative cosmological constant for a particular choice of conformal boundary conditions: the conformal class of the induced metric at the boundary is kept fixed and the mean extrinsic curvature is constrained to be one. Such specific conformal boundary conditions define so-called Bryant surfaces, which can be classified completely in terms of holomorphic maps from Riemann surfaces into the spinor bundle. To study the observables and gauge symmetries of the resulting bulk plus boundary system, we will introduce an extended phase space, where these holomorphic maps are now part of the gravitational bulk plus boundary phase space. The physical phase space is obtained by introducing two sets of Kac-Moody currents, which are constrained to vanish. The constraints are second-class and the corresponding Dirac bracket yields an infinite-dimensional deformation of the Heisenberg algebra for the spinor-valued surface charges. Finally, we compute the Poisson algebra among the generators of conformal diffeomorphisms and demonstrate that there is no central charge. Although the central charge vanishes and the boundary CFT is likely non-unitary, we will argue that a version of the Cardy formula still applies in this context, such that the entropy of the BTZ black hole can be derived from the degeneracy of the eigenstates of quasi-local energy. © 2020, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer
Additional Information: copyright of this article belongs to Springer
Keywords: AdS-CFT CorrespondenceChern-Simons TheoriesClassical Theories of GravityModels of Quantum Gravity
Department/Centre: UG Programme
Date Deposited: 06 Oct 2020 06:02
Last Modified: 06 Oct 2020 06:02
URI: http://eprints.iisc.ac.in/id/eprint/65172

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