Holographic Lorentz and Carroll Frames

TL;DR

The paper investigates three-dimensional gravity in AdS and flat spacetimes under a covariant Bondi gauge that promotes a boundary Cartan frame to a physical boundary degree of freedom. By exploiting ambiguities in the presymplectic structure, it derives two consistent prescriptions: one reproducing the Fefferman–Graham structure with a Weyl anomaly and the other yielding frame-rotations as boundary symmetries and a finite flat limit that relocates the anomaly to the Lorentz/ Carroll sector. It shows that the holographic Weyl anomaly and a Lorentz (or Carroll boost) anomaly are cohomologically equivalent representatives in the same anomaly class, with the Brown–Henneaux central charge $c=\frac{3}{2k\mathcal{G}}$ appearing in the Lorentz/Carlol sectors. In the conformal gauge, charges become integrable, Weyl transformations are pure gauge, and the Lorentz/Carroll charges encode the physical anomalous symmetries, including central extensions in the corresponding algebras. The flat limit reveals a Carrollian holography at null infinity, predicting a Carroll boost anomaly in dual conformal Carrollian field theories and connecting to $\mathrm{BMS}_3$-invariant structures, with potential links to celestial holography and higher-dimensional extensions.

Abstract

Relaxing the Bondi gauge, the solution space of three-dimensional gravity in the metric formulation has been shown to contain an additional free function that promotes the boundary metric to a Lorentz or Carroll frame, in asymptotically AdS or flat spacetimes. We pursue this analysis and show that the solution space also admits a finite symplectic structure, obtained taking advantage of the built-in ambiguities. The smoothness of the flat limit of the AdS symplectic structure selects a prescription in which the holographic anomaly appears in the boundary Lorentz symmetry, that rotates the frame. This anomaly turns out to be cohomologically equivalent to the standard holographic Weyl anomaly and survives in the flat limit, thus predicting the existence of quantum anomalies in conformal Carrollian field theories. We also revisit these results in the Chern--Simons formulation, where the prescription for the symplectic structure admitting a smooth flat limit follows from the variational principle, and we compute the charge algebra in the boundary conformal gauge.