  We discuss non-relativistic conformal algebras generalizing the Schr\"odinger
algebra. One instance of these algebras is a conformal, acceleration-extended,
Galilei algebra, which arises also as a contraction of the relativistic
conformal algebra. In two dimensions, this admits an "exotic" central
extension, whereby boosts do not commute. We study general properties of
non-relativistic conformal field theories with such symmetry. We realize
geometrically the symmetry in terms of a metric invariant under the exotic
conformal Galilei algebra, although its signature is neither Lorentzian nor
Euclidean. We comment on holographic-type calculations in this background.
