Weyl charges in asymptotically locallyAdS3spacetimes

Conservation and integrability in lower-dimensional gravity

“…Therefore, the Weyl rescaling part of the residual gauge diffeomorphisms is not in the asymptotic symmetry algebra. This observation contrasts with results obtained in the Fefferman-Graham gauge [27,66] where the Weyl charge is non-vanishing and highlights the presence of a Weyl anomaly in the dual theory. However, this apparent discrepancy unveils some non-trivial dependence in the choice of gauge fixing to perform the analysis of asymptotics.…”

“…This picture naturally yields fluctuations of the boundary metric and induced quantum gravity on the boundary [53]. Finally, let us mention that a specific example which reinforces the physical relevance of this type of relaxed boundary conditions has been investigated recently in asymptotically locally AdS 3 spacetimes, where the nonconservation of the charges has been interpreted as an anomalous Ward-Takahashi identity in the dual theory [66].…”

“…After performing the holographic renormalization of the action and the symplectic structure in Bondi gauge using covariant counter-terms [27,53,85,86,98] and corner terms [26,98], we obtain the gravitational charges associated with the solution space derived in [42,43] that includes fluctuating boundary structure. Again, we find the appropriate field-dependent redefinition of the parameters to render the charges integrable [12,30,66,[89][90][91]. In asymptotically locally AdS 3 spacetimes (respectively asymptotically locally flat spacetimes), the asymptotic symmetry algebra is given by a Lie algebroid [99] with a one-dimensional base space parametrized by the time u on the boundary and with a Diff(S 1 )⊕Diff(S 1 ) (respectively BMS 3 ) algebra at each value of u.…”

“…In this work, we construct the maximal asymptotic symmetry algebra that one can obtain in two-dimensional gravity theories by imposing only partial gauge fixing on the components of the metric and very mild falloffs. After a renormalization procedure of the on-shell action and the symplectic structure involving covariant counter-terms [53,[85][86][87][88], we obtain finite charge expressions that we render integrable through a field-dependent redefinition of the symmetry parameters [12,30,66,[89][90][91]. The asymptotic symmetry algebra is given by the direct sum of three abelian Lie algebras of smooth functions…”

“…Nevertheless, in the absence of propagating degrees of freedom passing through the boundary, it is physically expected that a slicing of the phase space for which the charges are integrable can be found [30]. In equations (3.44) and (4.38) below, we will see two explicit examples of field-dependent redefinition as in (2.12) (see also [66,[89][90][91] for other examples).…”