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.
Highlights
It may be argued that for ultra-relativistic field theories, even if existence of fixed points cannot be proven, one is on safe grounds since in some limit the relativistic theory is approached and RG flow would be well behaved
Section three is devoted to holographic calculations where we find conformal anomaly of the ultra-relativistic theory
The generators E, P, B, D, F, G are respectively energy, momentum, boost, dilation, acceleration and special conformal transformation (for their precise definitions see below (2.3)). Note that this algebra is isomorphic to Galilean Conformal Algebra (GCA) [24] by switching the space and time coordinates
Summary
In this paper we are interested in ultra-relativistic contraction of 2d CFTs, which is achievable if speed of light tends to zero. The generators E, P, B, D, F, G are respectively energy, momentum, boost, dilation, acceleration and special conformal transformation (for their precise definitions see below (2.3)) Note that this algebra is isomorphic to Galilean Conformal Algebra (GCA) [24] by switching the space and time coordinates. → 0 corresponds to contraction of time in the boundary as t → ǫt Using this correspondence one can study some aspects of gravity in the three dimensional asymptotically flat spacetimes by using two dimensional ultra-relativistically contracted CFT. For example a quasi local stress tensor for asymptotically flat spacetimes is achievable if we start with energy momentum of a CFT and contract it [26]. Where + and − correspond to light-cone coordinates in both of the theories
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