Lifshitz Scale Anomalies

Abstract

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.

58 pages, 5 appendices

References in corpus (9)

• Quantum criticality
• Topological Order and Conformal Quantum Critical Points
• Quantum Criticality
• Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
• Lifshitz Gravity for Lifshitz Holography
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• Horava-Lifshitz Black Hole Hydrodynamics
• Lifshitz Superfluid Hydrodynamics

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