  Holography for Lifshitz space-times corresponds to dual field theories on a
fixed torsional Newton-Cartan (TNC) background. We examine the coupling of
non-relativistic field theories to TNC backgrounds and uncover a novel
mechanism by which a global U(1) can become local. This involves the TNC vector
$M_\mu$ which sources a particle number current, and which for flat NC
space-time satisfies $M_{\mu}=\partial_{\mu}M$ with a Schroedinger symmetry
realized on $M$. We discuss various toy model field theories on flat NC
space-time for which the new mechanism leads to extra global space-time
symmetries beyond the generic Lifshitz symmetry, allowing for an enhancement to
Schroedinger symmetry. On the holographic side, the source $M$ also appears in
the Lifshitz vacuum with exactly the same properties as for flat NC space-time.
In particular, the bulk diffeomorphisms that preserve the boundary conditions
realize a Schroedinger algebra on $M$, allowing for a conserved particle number
current. Finally, we present a probe action for a complex scalar field on the
Lifshitz vacuum, which exhibits Schroedinger invariance in the same manner as
seen in the field theory models.
