The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic
limit of the symmetries of a relativistic Conformal Field Theory in any
dimensions. It is known to be infinite-dimensional in all spacetime dimensions.
In particular, the 2d GCA emerges out of a scaling limit of linear combinations
of two copies of the Virasoro algebra. In this paper, we find metrics in
dimensions greater than two which realize the finite 2d GCA (the global part of
the infinite algebra) as their isometry by systematically looking at a
construction in terms of cosets of this finite algebra. We list all possible
sub-algebras consistent with some physical considerations motivated by earlier
work in this direction and construct all possible higher dimensional
non-degenerate metrics. We briefly study the properties of the metrics
obtained. In the standard one higher dimensional "holographic" setting, we find
that the only non-degenerate metric is Minkowskian. In four and five
dimensions, we find families of non-trivial metrics with a rather exotic
signature. A curious feature of these metrics is that all but one of them are
Ricci-scalar flat.Comment: 20 page
