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Peer-reviewedCC BY 4.0The European Physical Journal C

Trace anomaly for a conformal 2D vector field model

  • Samuel W. P. Oliveira1
  • Ilya L. Shapiro2
  1. 1PPGCosmo, Universidade Federal do Espírito Santo
  2. 2Universidade Federal de Juiz de Fora
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Abstract

The trace anomaly and anomaly-induced action are evaluated for the two-dimensional 2 D 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 → 2 D → 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 ≥ 4 D ≥ 4 . For comparison and completeness, we also evaluate anomalies for conformal scalar and fermions, also in the presence of auxiliary external scalars.

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Cite

BibTeXRIS
BibTeX
@article{oliveira2026trace,
  title = {{Trace anomaly for a conformal 2D vector field model}},
  author = {Samuel W. P. Oliveira and Ilya L. Shapiro},
  journal = {The European Physical Journal C},
  year = {2026},
  month = oct,
  doi = {10.1140/epjc/s10052-026-16361-0},
  url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16361-0},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Trace anomaly for a conformal 2D vector field model
AU  - Samuel W. P. Oliveira
AU  - Ilya L. Shapiro
PY  - 2026
DA  - 2026/10/16
JO  - The European Physical Journal C
DO  - 10.1140/epjc/s10052-026-16361-0
UR  - https://link.springer.com/article/10.1140/epjc/s10052-026-16361-0
AB  - The trace anomaly and anomaly-induced action are evaluated for the two-dimensional 2 D 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 → 2 D → 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 ≥ 4 D ≥ 4 . For comparison and completeness, we also evaluate anomalies for conformal scalar and fermions, also in the presence of auxiliary external scalars.
SN  - 1434-6044
SN  - 1434-6052
ER  -