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In this note we investigate the anomalous breaking of anisotropic scalingsymmetry in a non-relativistic field theory with dynamical exponent z=2. Ongeneral 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 freefield theory which is second order in time and fourth order in spatialderivatives. We find that one of the two central charges vanishes.Interestingly, this is also true for strongly coupled non-relativistic fieldtheories with a geometric dual described by a metric and a massive vectorfield.

Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model