Extended-BMS Anomalies and Flat Space Holography

TL;DR

The paper develops an intrinsic, boundary-only BRST framework for the extended BMS (eBMS) group at null infinity ${\mycal I}^+$, showing that the boundary shear is encoded in the Carrollian boundary connection and that a conformal Carroll gauge isolates the eBMS residual symmetry. It classifies eBMS-invariant Lagrangians and anomalies using BRST cohomology, finding a single topological 3d Lagrangian and anomalies confined to the superrotation sector with three central charges, two of which are physical. Through holographic matching, the authors relate the boundary central charges to bulk gravity data, obtaining $c_\xi=c_{\bar\xi}=1/(4\pi G)$ and linking the absence of supertranslations to the tree-level validity of Weinberg’s soft graviton theorem. These results provide non-perturbative support for flat-space holography, illustrate a dimensional reduction to a 2d boundary theory, and offer a concrete boundary derivation of eBMS structure independent of bulk considerations.

Abstract

We classify the Lagrangians and anomalies of an extended BMS field theory using BRST methods. To do so, we establish an intrinsic gauge-fixing procedure for the geometric data, which allows us to derive the extended BMS symmetries and the correct transformation law of the shear, encoded in the connection. Our analysis reveals that the invariant Lagrangians are always topological, thereby reducing the 4d bulk to a 2d boundary theory. Moreover, we find that supertranslations are anomaly-free, while superrotations exhibit independent central charges. This BMS field theory is dual to Einstein gravity in asymptotically flat spacetimes when the superrotation anomalies coincide and are dictated by the bulk. Meanwhile, the absence of supertranslation anomalies aligns with Weinberg's soft graviton theorem being tree-level exact. This work provides a first-principle derivation of the structure of the null boundary field theory, intrinsic and independent of bulk considerations, offering further evidence for the holographic principle in flat space, and its dimensional reduction.