Anisotropic Weyl invariance

Abstract

We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates "scaling like time" is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry.

15 pages, matches journal version

References in corpus (5)

• Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Lifshitz Gravity for Lifshitz Holography
• Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization
• Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory

Cited by in corpus (2)

• On the Heat Kernel and Weyl Anomaly of Schrödinger invariant theory
• Aspects of $(d+D)$-dimensional Anisotropic Conformal Gravity