  In this note we investigate the anomalous breaking of anisotropic scaling
symmetry in a non-relativistic field theory with dynamical exponent z=2. On
general grounds, one can show that there exist two possible "central charges"
which characterize the breaking of scale invariance. Using heat kernel methods,
we compute these two central charges in the quantum Lifshitz model, a free
field theory which is second order in time and fourth order in spatial
derivatives. We find that one of the two central charges vanishes.
Interestingly, this is also true for strongly coupled non-relativistic field
theories with a geometric dual described by a metric and a massive vector
field.
