Anomalies for Galilean fields

Abstract

We initiate a systematic study of `t Hooft anomalies in Galilean field theories, focusing on two questions therein. In the first, we consider the non-relativistic theories obtained from a discrete light-cone quantization (DLCQ) of a relativistic theory with flavor or gravitational anomalies. We find that these anomalies survive the DLCQ, becoming mixed flavor/boost or gravitational/boost anomalies. We also classify the pure Weyl anomalies of Schrödinger theories, which are Galilean conformal field theories (CFTs) with $z=2$. There are no pure Weyl anomalies in even spacetime dimension, and the lowest-derivative anomalies in odd dimension are in one-to-one correspondence with those of a relativistic CFT in one dimension higher. These results classify many of the anomalies that arise in the field theories dual to string theory on Schrödinger spacetimes.

22 pages, 1 figure; v2: Added some comments

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• Renormalization properties of a Galilean Wess-Zumino model
• Hydrodynamic effective field theories with discrete rotational symmetry
• BMS Field Theories and Weyl Anomaly
• Spinor fields in general Newton-Cartan backgrounds
• Quantization of Interacting Galilean Field theories
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Nonrelativistic trace and diffeomorphism anomalies in particle number background
• Torsion and anomalies in the warped limit of Lifschitz theories
• Non-Relativistic Supersymmetry on Curved Three-Manifolds
• Galilean fermions: Classical and quantum aspects
• Non-relativistic Conformal Field Theory in the Presence of Boundary
• Canonical Formulation for a Non-relativistic Spinning Particle Coupled to Gravity
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Developments in non-relativistic field theory and complexity