Extended-BMS Anomalies and Flat Space Holography

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.