The BMS/GCA correspondence

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We find a surprising connection between asymptotically flat space-times and non-relativistic conformal systems in one lower dimension. The BMS group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean Conformal Algebra which is of relevance to non-relativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit of a radially infalling null ray inspired by non-relativistic scaling and obtain a flat metric. The 4D BMS algebra is also discussed and found to be the same as another class of GCA, called the semi-GCA, in three dimensions. We propose a general BMS/GCA correspondence. Some consequences are discussed.