Non-relativistic scale anomalies. (English) Zbl 1388.83546
Summary: We extend the cohomological analysis in our work [ibid. 2015, No. 2, Paper No. 78, 58 p. (2015; Zbl 1388.83037)] of anisotropic Lifshitz scale anomalies. We consider non-relativistic theories with a dynamical critical exponent \(z=2\) with or without non-relativistic boosts and a particle number symmetry. We distinguish between cases depending on whether the time direction does or does not induce a foliation structure. We analyse both 1 + 1 and 2 + 1 spacetime dimensions. In 1 + 1 dimensions we find no scale anomalies with Galilean boost symmetries. The anomalies in 2 + 1 dimensions with Galilean boosts and a foliation structure are all B-type and are identical to the Lifshitz case in the purely spatial sector. With Galilean boosts and without a foliation structure we find also an A-type scale anomaly. There is an infinite ladder of B-type anomalies in the absence of a foliation structure with or without Galilean boosts. We discuss the relation between the existence of a foliation structure and the causality of the field theory.
MSC:
| 83C80 | Analogues of general relativity in lower dimensions |
Citations:
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