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Lifshitz Scale Anomalies
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We analyse scale anomalies in Lifshitz field theories, formulated as the relative cohomology of the scaling operator with respect to foliation preserving diffeomorphisms. We construct a detailed framework that enables us to calculate the anomalies for any number of spatial dimensions, and for any value of the dynamical exponent. We derive selection rules, and establish the anomaly structure in diverse universal sectors. We present the complete cohomologies for various examples in one, two and three space dimensions for several values of the dynamical exponent. Our calculations indicate that all the Lifshitz scale anomalies are trivial descents, called B-type in the terminology of conformal anomalies. However, not all the trivial descents are cohomologically non-trivial. We compare the conformal anomalies to Lifshitz scale anomalies with a dynamical exponent equal to one.
Forward citations
Cited by 2 Pith papers
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The anisotropic chiral boson
An anisotropic (Lifshitz-like) chiral boson has an exact partition function generated by partitions into z-th powers, plus a nonlocal conformal symmetry.
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A (1+1)-dimensional Lifshitz Weyl Anomaly From a Schr$\mathrm{\ddot{o}}$dinger-invariant Non-relativistic Chern-Simons Action
The torsional Chern-Simons term in a non-relativistic Schrodinger-invariant action reproduces, in form, the 1+1 Lifshitz Weyl anomaly on the boundary, though its coefficient is not fixed.
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