Phys. Rev. D 103, 046003 (2021)                                  arXiv link

Weyl charges in asymptotically locally AdS₃ spacetimes

Francesco Alessio^1,2, Glenn Barnich², Luca Ciambelli², Pujian Mao³, and Romain Ruzziconi⁴

1 Dipartimento di Fisica “E. Pancini” and INFN, Università degli studi di Napoli “Federico II”, I-80125 Napoli, Italy

2 Université Libre de Bruxelles and International Solvay Institutes CP 231, B-1050 Brussels, Belgium

3 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China

4 Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8, A-1040 Vienna, Austria

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 with Weyl transformations are nonvanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional nontrivial 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.