Aspects of Flat/CCFT Correspondence

TL;DR

The paper investigates flat-space holography by proposing a Flat/CCFT correspondence in which the bulk asymptotically flat limit corresponds to a contraction of the boundary CFT. Using this dictionary, it shows that the CCFT_2 Cardy-like entropy arises from contracting a modified CFT_2 Cardy formula, which in the bulk reproduces the inner-horizon (cosmological horizon) entropy of BTZ-related geometries. An explicit CCFT entropy formula, $S_{CCFT} = 2\pi \left( C_{LL} \sqrt{\frac{M_0}{2 C_{LM}}} + L_0 \sqrt{\frac{C_{LM}}{2 M_0}} \right)$, is derived, and its consistency with the alternative Cardy form is discussed along with bulk charge relations. The results support flat-space holography and outline avenues to higher dimensions (e.g., BMS_4) and CCFT_3, while noting that the microscopic interpretation of inner-horizon counting remains an open question.

Abstract

Flat/CCFT is a correspondence between gravity in asymptotically flat backgrounds and a field theory which is given by contraction of conformal field theory. In order to find a dictionary for Flat/CCFT correspondence one can start from the AdS/CFT and take the contraction of CFT in the boundary as the dual description of the flat-space limit (zero cosmological constant limit) of the asymptotically AdS spacetimes in the bulk side. In this paper we show that the Cardy-like formula of CCFT_2 is given by contraction of a proper formula in the CFT_2. This formula is the modified Cardy formula which gives the entropy of inner horizon of BTZ black holes.