Scale anomalies in non-relativistic field theories in 2+1 dimensions

TL;DR

This paper investigates scale anomalies in non-relativistic 2+1 dimensional field theories, deriving the anomaly from the one-loop effective potential for bosons with delta interactions and Chern-Simons terms, and finds that anyons exhibit no anomaly at certain orders.

Contribution

It provides a direct derivation of the energy-momentum tensor anomaly in non-relativistic theories with delta interactions and Chern-Simons terms, highlighting the absence of anomaly in anyons at specific orders.

Findings

Anomaly derived from one-loop effective potential for bosons.

Anomaly also derived with Chern-Simons interactions.

No scale anomaly observed in anyons at one-loop and second order in statistical angle.

Abstract

{}From the one-loop effective potential for a gas of non-relativistic bosons in two spatial dimensions interacting via a delta-function potential at zero-temperature and finite chemical potential, the anomaly of the energy-momentum tensor follows directly. It is also similarly derived when the bosons have an additional Chern-Simons interaction. In the special case of anyons, the scale anomaly vanishes to one-loop order in the effective potential and also to second order in the statistical angle.