Abstract
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D=4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.
Highlights
1.1 The Strominger TriangleOf late, there has been a resurgence in the study of quantum gravity in asymptotically flat spacetimes
If we look at the Asymptotic Symmetry Group at the null boundary of flat space, this becomes the infinite dimensional BMS3 group and the corresponding algebra is given by cL m(m2 12
We investigated the symmetries of the equations of motion for these Carrollian gauge theories and found that there is the emergence of infinite dimensional Carrollian conformal symmetry in D = 4 in all the sectors that we discussed
Summary
There has been a resurgence in the study of quantum gravity in asymptotically flat spacetimes This renewed interest is primarily due to Strominger’s new insights [1] into the apparently unrelated physics of asymptotic symmetries, soft theorems in quantum field theory and the so-called memory effects. New soft-graviton theorems related to Ward identities arising out of diagonal super-rotation invariance of the gravitational S-matrix have been discovered [9], leading to a Virasoro invariance of the quantum gravity S-matrix [10]. There has been the discovery of a new gravitational memory effect, called the spin memory which are related to super-rotations [13] These again are related to the new soft graviton theorems by a Fourier transform in the time direction. These charges may go a long way in a resolution of the information loss paradox
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