TY - GEN

T1 - Newton–Cartan trace anomalies and renormalization group flows

AU - Auzzi, Roberto

PY - 2018

Y1 - 2018

N2 - I will discuss trace anomalies for non-relativistic Schrödinger theories in 2+1 dimensions coupled to a Newton–Cartan gravity background, which is used as a source of the energy-momentum tensor. The motivation is to identify candidates for a possible non-relativistic version of the a-theorem for theories with RG flows interpolating between an UV and an IR Schroedinger-invariant non-relativistic conformal fixed points. I will first discuss the general structure of the anomaly, which is determined by the Wess–Zumino consistency condition. Then I will present an explicit calculation for the anomaly in the case of a free scalar and of a free fermion, using heat kernel. There is a type A anomaly which is proportional to 1/m, where m is the mass of the particle. In analogy with the relativistic case, the irreversibility properties of the renormalization group can also be investigated by studying the Wess–Zumino consistency conditions for the trace anomaly of the theory in a Newton Cartan background with space-time dependent couplings.

AB - I will discuss trace anomalies for non-relativistic Schrödinger theories in 2+1 dimensions coupled to a Newton–Cartan gravity background, which is used as a source of the energy-momentum tensor. The motivation is to identify candidates for a possible non-relativistic version of the a-theorem for theories with RG flows interpolating between an UV and an IR Schroedinger-invariant non-relativistic conformal fixed points. I will first discuss the general structure of the anomaly, which is determined by the Wess–Zumino consistency condition. Then I will present an explicit calculation for the anomaly in the case of a free scalar and of a free fermion, using heat kernel. There is a type A anomaly which is proportional to 1/m, where m is the mass of the particle. In analogy with the relativistic case, the irreversibility properties of the renormalization group can also be investigated by studying the Wess–Zumino consistency conditions for the trace anomaly of the theory in a Newton Cartan background with space-time dependent couplings.

KW - Anomalies

KW - Mathematics (all)

KW - Nonrelativistic field theories

KW - Renormalization group flow

KW - Anomalies

KW - Mathematics (all)

KW - Nonrelativistic field theories

KW - Renormalization group flow

UR - http://hdl.handle.net/10807/131805

UR - http://www.springer.com/series/10533

U2 - 10.1007/978-981-13-2179-5_33

DO - 10.1007/978-981-13-2179-5_33

M3 - Conference contribution

SN - 9789811321788

VL - 255

T3 - SPRINGER PROCEEDINGS IN MATHEMATICS & STATISTICS

SP - 421

EP - 429

BT - Springer Proceedings in Mathematics and Statistics

T2 - International Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017

Y2 - 19 June 2017 through 25 June 2017

ER -