On Newton-Cartan trace anomalies

Abstract

We classify the trace anomaly for parity-invariant non-relativistic Schrödinger theories in 2+1 dimensions coupled to background Newton-Cartan gravity. The general anomaly structure looks very different from the one in the z=2 Lifshitz theories. The type A content of the anomaly is remarkably identical to that of the relativistic 3+1 dimensional case, suggesting the conjecture that an a-theorem should exist also in the Newton-Cartan context. Erratum: due to an overcounting of the number of linearly-independent terms in the basis, the type A anomaly disappears if Frobenius condition is imposed. See appended erratum for details. This crucial mistake was pointed out to us in arXiv:1601.06795.

16 pages, V2:few equations corrected (final results unchanged), references added, typos, V3: erratum included

References in corpus (7)

• Gravity duals for non-relativistic CFTs
• Holographic c-theorems in arbitrary dimensions
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Lifshitz Space-Times for Schroedinger Holography
• Revisiting non-relativistic limits
• Newton-Cartan (super)gravity as a non-relativistic limit
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Cited by in corpus (11)

• Anomalies for Galilean fields
• Non-Relativistic Scale Anomalies
• Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization
• Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory
• On Newton-Cartan local renormalization group and anomalies
• Heat kernel for Newton-Cartan trace anomalies
• Newton-Cartan, Galileo-Maxwell and Kaluza-Klein
• Gravitational anomalies on the Newton-Cartan background
• Spontaneous Breaking of Non-Relativistic Scale Symmetry
• Nonrelativistic trace and diffeomorphism anomalies in particle number background
• Trace anomaly for non-relativistic fermions