Carrollian c functions and flat space holographic RG flows in BMS₃/CCFT₂

Abstract

We discuss c functions and their holographic counterpart for two-dimensional field theories with Carrollian conformal fixed points in the UV and the IR. Specifically, we construct asymptotically flat domain wall solutions of three-dimensional Einstein-dilaton gravity that model holographic renormalization group (RG) flows between BMS3 invariant UV and IR fixed points. We prove three theorems for such flows: (1) for every holographic RG flow in AdS3, there is a corresponding one in flat space, (2) the BMS central charge in the UV cannot be smaller than in the IR, and (3) the UV/IR ratio of Virasoro central charges is identical to the UV/IR ratio of corresponding BMS central charges. Finally, we tentatively propose a Casini-Huerta-like c functions for BMS3-invariant quantum field theories, inspired by the AdS3/CFT2 relation between monotonicity of the c function and the quantum null energy condition.