  The asymptotic group of symmetries at null infinity of flat spacetimes in
three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS)
group. This has recently been shown to be isomorphic to non-relativistic
conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA)
in 2d and a closely related non-relativistic algebra in 3d [1]. We provide a
better understanding of this surprising connection by providing a spacetime
interpretation in terms of a novel contraction. The 2d GCA, obtained from a
linear combination of two copies of the Virasoro algebra, is generically
non-unitary. The unitary subsector previously constructed had trivial
correlation functions. We consider a representation obtained from a different
linear combination of the Virasoros, which is relevant to the relation with the
BMS algebra in three dimensions. This is realised by a new space-time
contraction of the parent algebra. We show that this representation has a
unitary sub-sector with interesting correlation functions. We discuss
implications for the BMS/GCA correspondence and show that the flat space limit
actually induces precisely this contraction on the boundary conformal field
theory. We also discuss aspects of asymptotic symmetries and the consequences
of this contraction in higher dimensions.
