Rindler/Contracted-CFT Correspondence

Abstract: Taking the flat-space limit (zero cosmological constant limit) of the Rindler-AdS spacetime yields the Rindler metric. According to the proposal of Flat/contracted-CFT correspondence, the flat-space limit on the bulk side of asymptotically AdS spacetimes corresponds to the contraction of the conformal field theory on the boundary. We use this proposal for the Rindler-AdS/CFT correspondence and propose a dual theory for the Rindler spacetime, which is a contracted conformal field theory (CCFT). We show that the two-dimensional CCFT symmetries exactly predict the same two-point functions that one may find by taking the flat-space limit of three-dimensional Rindler-AdS holographic results. Using the Flat/CCFT proposal, we also calculate the three-dimensional Rindler energy-momentum tensor. Since the near horizon geometry of non-extreme black holes has a Rindler part, we note that it is plausible to find a dual CCFT at the horizon of non-extreme black holes. By using our energy-momentum tensor, we find the correct mass of non-rotating BTZ and show that the Cardy-like formula for CCFT yields the Bekenstein-Hawking entropy of non-extreme BTZ. Our current work is the first step towards describing the entropy of non-extreme black holes in terms of CCFTs microstates which live on the horizon.