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arXiv · 2010.15452

Weyl Charges in Asymptotically Locally AdS$_3$ Spacetimes

Francesco Alessio·Glenn Barnich·Luca Ciambelli·Pujian Mao·Romain Ruzziconi
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Abstract

We discuss an enhancement of the Brown-Henneaux boundary conditions in three-dimensional AdS General Relativity to encompass Weyl transformations of the boundary metric. The resulting asymptotic symmetry algebra, after a field-dependent redefinition of the generators, is a direct sum of two copies of the Witt algebra and the Weyl abelian sector. The charges associated to Weyl transformations are non-vanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional non-trivial central extension in the Weyl sector, related to the well-known Weyl anomaly. We then construct the holographic Weyl current and show that it satisfies an anomalous Ward-Takahashi identity of the boundary theory.

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Francesco Alessio, Glenn Barnich, Luca Ciambelli, Pujian Mao, Romain Ruzziconi. 2020-10-29. Weyl Charges in Asymptotically Locally AdS$_3$ Spacetimes. https://doi.org/10.1103/physrevd.103.046003

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