Aspects of Ultra-Relativistic Field Theories via Flat-space Holography

TL;DR

The paper extends holography to asymptotically flat spacetimes by leveraging flat-space holography to study ultra-relativistic CFTs in 2d. It derives the ultra-relativistic conformal anomaly via a BMS-gauge holographic setup and demonstrates that the trace is governed by the central charge c_M, with c_L vanishing due to parity. It further constructs a holographic C-function that monotonically decreases from UV to IR along RG flow, using the null energy condition and the flat-space limit of AdS3/CFT2. These results illuminate the structure of ultra-relativistic boundary theories and their gravitational duals, providing a concrete analogue of c-theorems in flat spacetimes.

Abstract

Recently it was proposed that asymptotically flat spacetimes have a holographic dual which is an ultra-relativistic conformal field theory. In this paper, we obtain the conformal anomaly for such a theory via the flat-space holography technique. Furthermore, using flat-space holography we obtain a C-function for this theory which is monotonically decreasing from the UV to the IR by employing the null energy condition in the bulk.