Trace anomaly for a conformal 2D vector field model

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.