Anomaly effective actions for 4d š¯’©=1 superconformal field theories
Abstract
We present a comprehensive analysis of the Wess-Zumino anomaly effective action of four-dimensional š¯’©=1 superconformal field theories in components. After reviewing the coset construction of the Wess-Zumino action in the presence of an unbroken subgroup, the gauging of the conformal algebra and the Wess-Zumino effective action for non-supersymmetric conformal field theories with a U(1) symmetry in two and four dimensions, we revisit the superconformal anomalies of š¯’©=1 conformal supergravity. Solving the Wess-Zumino consistency conditions we determine both the bosonic and fermionic superconformal anomalies in a two-parameter family of schemes, to quadratic order in the gravitino. Turning on a chiral compensator multiplet and identifying a local super-PoincarĆ© subalgebra of the conformal supergravity algebra without gauge-fixing the coset symmetries, we employ the coset construction and the superconformal anomalies in order to evaluate the Wess-Zumino action for generic š¯’©=1 superconformal field theories coupled to conformal supergravity. By construction, this action reproduces the Weyl, R-symmetry, and S-supersymmetry coset anomalies, but its transformation under the unbroken PoincarĆ© supersymmetry differs from the corresponding anomaly of the conformal supergravity functional. We show that there exists a local functional of the coset-invariant old-minimal fields that, when added to the Wess-Zumino action, results in a generalized Wess-Zumino action that reproduces all anomalies of the conformal supergravity functional. The same local functional enables us to determine the super-Weyl anomalies and the Wess-Zumino action of old-minimal supergravity, providing a component version of the known superspace Wess-Zumino action.
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BibTeX
@misc{panopoulos2026anomaly,
title = {{Anomaly effective actions for 4d $\mathcalN=1$ superconformal field theories}},
author = {Pantelis Panopoulos and Ioannis Papadimitriou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06842},
eprint = {2611.06842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06842},
}
RIS
TY - UNPB
TI - Anomaly effective actions for 4d š¯’©=1 superconformal field theories
AU - Pantelis Panopoulos
AU - Ioannis Papadimitriou
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06842
UR - https://arxiv.org/abs/2611.06842
AB - We present a comprehensive analysis of the Wess-Zumino anomaly effective action of four-dimensional š¯’©=1 superconformal field theories in components. After reviewing the coset construction of the Wess-Zumino action in the presence of an unbroken subgroup, the gauging of the conformal algebra and the Wess-Zumino effective action for non-supersymmetric conformal field theories with a U(1) symmetry in two and four dimensions, we revisit the superconformal anomalies of š¯’©=1 conformal supergravity. Solving the Wess-Zumino consistency conditions we determine both the bosonic and fermionic superconformal anomalies in a two-parameter family of schemes, to quadratic order in the gravitino. Turning on a chiral compensator multiplet and identifying a local super-PoincarĆ© subalgebra of the conformal supergravity algebra without gauge-fixing the coset symmetries, we employ the coset construction and the superconformal anomalies in order to evaluate the Wess-Zumino action for generic š¯’©=1 superconformal field theories coupled to conformal supergravity. By construction, this action reproduces the Weyl, R-symmetry, and S-supersymmetry coset anomalies, but its transformation under the unbroken PoincarĆ© supersymmetry differs from the corresponding anomaly of the conformal supergravity functional. We show that there exists a local functional of the coset-invariant old-minimal fields that, when added to the Wess-Zumino action, results in a generalized Wess-Zumino action that reproduces all anomalies of the conformal supergravity functional. The same local functional enables us to determine the super-Weyl anomalies and the Wess-Zumino action of old-minimal supergravity, providing a component version of the known superspace Wess-Zumino action.
ER -