Stress tensor correlators of $$\hbox {CCFT}_2$$ CCFT 2 using flat-space holography

Abstract

We use the correspondence between three-dimen sional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT 2 . On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for the four-dimensional case, where there is no ChernSimons formulation for the bulk theory.

Flat-space holography and correlators of Robinson–Trautman stress tensor

“…Our approach in this paper is similar to [10,11,12,13]. We start from some asymptotically flat solutions and find the asymptotically AdS spacetimes whose flat-space limit leads to the original asymptotically flat metric.…”

“…We have used the above approach for BMSFT 2 in papers [10,11,13] and for the quasi-local stress tensor of the Kerr black hole in [12]. In this paper we apply our method for a class of fourdimensional asymptotically flat spacetimes known as Robinson-Trautman (RT) solutions [20] (see also [21] ).…”

“…Although, taking the flat-space limit from the metric components is straightforward but stress tensor components are either zero or singular after taking the naive flat-space limit. Hence, similar to [10,11,12,13], we first multiply appropriate powers of AdS radius and then take the flat-space limit. In order to show that our proposed stress tensor is correct, we shall use it to compute the conserved charges of symmetry generators.…”

“…Currently we do not know a clear justification of this proposal but it should be similar to the non-relativistic holography discussed in [26]. In our previous works [10,11,12,13], we have successfully used this idea to compute charges by using proposed flat-space stress tensor. Our observation shows that if we find an asymptotically flat spacetimes by taking flat-space limit from an asymptotically AdS spacetimes, the dual BMSFT lives on a spacetime which has the same metric as the spacetime which CFT lives on it but the AdS radius should be replaced by proper powers of Newton's constant.…”

Complexity growth in flat spacetimes

“…The interesting point is that this formula yields the entropy of three-dimensional flat space cosmology (FSC), which is given by taking the flat space limit from the Banados, Teitelboim and Zanelli (BTZ) black holes. The universal structure of the correlation functions of BMSFT 2 and BMSFT 3 has been studied in [9][10][11][12]. The entanglement entropy formula and also the holographic interpretation of this formula in the context of flat/BMSFT have been studied in [13][14][15][16][17][18][19][20].…”