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

TL;DR

This paper explores holographic RG flows between BMS3 invariant fixed points in flat space, establishing theorems relating BMS and Virasoro central charges, and proposes a new c-function for BMS3-invariant theories.

Contribution

It constructs flat space holographic RG flow models and proves theorems linking BMS3 and AdS3 central charges, introducing a novel c-function for BMS3 field theories.

Findings

Holographic RG flows in flat space correspond to those in AdS3.

BMS central charge in UV is not smaller than in IR.

The UV/IR ratio of BMS central charges matches that of Virasoro central charges.

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 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.