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

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