Trace anomaly for a conformal 2D vector field model

TL;DR

This paper analyzes the trace anomaly in a 2D conformal vector field model, revealing a complex anomaly structure and discussing the implications of local conformal symmetry and gauge invariance in two dimensions.

Contribution

It provides a detailed calculation of the trace anomaly for a 2D vector theory, highlighting the singular limit and the anomaly's structure in dimensional regularization.

Findings

The anomaly expression has a rich structure similar to higher dimensions.

The 2D limit is singular but smooth in dimensional regularization.

Anomalies for scalars and fermions are also evaluated for comparison.

Abstract

The trace anomaly and anomaly-induced action are evaluated for the two-dimensional $2D$ vector theory with classical conformal symmetry. Implementing local conformal symmetry while preserving the gauge invariance requires either giving up locality of the classical action or, equivalently, introducing an auxiliary scalar field. The two-dimensional limit in such a theory is singular. However, in the dimensional regularization, the limit $D \to 2$ in the one-loop divergence is smooth. As a result, we arrive at the expression for anomaly, which has a rich general structure, typical for the dimensions $D \geq 4$. For comparison and completeness, we also evaluate anomalies for conformal scalar and fermions, also in the presence of auxiliary external scalars.