2017/03/31 by Karan Fernandes, Arpita Mitra
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Diffeomorphism #Field (mathematics) #Gauge (firearms) #Gauge anomaly #Gauge theory #Gravitation #Gravitational field #Introduction to gauge theory #Mathematical analysis #Mathematical physics #Mathematics #Mixed anomaly #Philosophy #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Quantum mechanics #TRACE (psycholinguistics) #Term (time) #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.96.085003
published as Phys. Rev. D 96, 085003 (2017) · 37 pages, no figures
arxiv created 2017/08/20 · openalex publication_date 2017/10/10 · arxiv updated 2017/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive the trace and diffeomorphism anomalies of the Schr"odinger field minimally coupled to the Newton-Cartan background using Fujikawa's path integral approach. This approach, in particular, enables us to calculate the one-loop contributions due to all the fields of the Newton-Cartan structure. We determine the coefficients and demonstrate that gravitational anomalies for this theory always arise in odd dimensions. Because of the gauge field contribution of the background, we find that in 2+1 dimensions, the trace anomaly contains terms which have a form similar to that of the 1+1 and 3+1 dimensional relativistic trace anomalies. The term similar to the 1+1 dimensional relativistic trace anomaly provides a type A contribution on Newton-Cartan backgrounds which satisfy the Frobenius condition, in contrast with the result of Lifshitz spacetimes. As an application, we demonstrate that the coefficient of this term satisfies a c-theorem condition.