Holographic Lorentz and Carroll Frames

TL;DR

This paper explores the extended solution space of three-dimensional gravity allowing boundary Lorentz or Carroll frames, revealing a holographic anomaly linked to boundary symmetries and its persistence in flat limits, with implications for quantum anomalies in Carrollian theories.

Contribution

It demonstrates the existence of a finite symplectic structure in the extended solution space and analyzes the holographic anomaly in boundary Lorentz symmetry, including its flat limit behavior.

Findings

The solution space admits a finite symplectic structure with boundary frame freedom.

The holographic anomaly appears in boundary Lorentz symmetry and is cohomologically equivalent to the Weyl anomaly.

The anomaly persists in the flat limit, indicating quantum anomalies in conformal Carrollian field theories.

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.