Abstract
We consider the 4-dimensional \( \mathcal{N} \) = 1 Lie superconformal algebra and search for completely “symmetric” (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant polynomial cubic in the generalized curvatures of superconformal gravity vanishes. Consequently, the associated Chern-Simons polynomial is a non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders in the independent fields of superconformal gravity and establish that it is BRST equivalent to the so-called superconformal a-anomaly. We briefly discuss the possibility that the superconformal c-anomaly also admits a similar Chern-Simons formulation and the potential holographic, 5-dimensional, interpretation of our results.
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Acknowledgments
C.I. is deeply grateful to M. Fröb for many patient and very helpful lessons about FieldsX.
This work is supported in part by the Italian Istituto Nazionale di Fisica Nucleare and by Research Projects, F.R.A. 2022 of the Università di Genova. The work of A.W. is supported by the UKRI Frontier Research Grant, underwriting the ERC Advanced Grant “Generalized Symmetries in Quantum Field Theory and Quantum Gravity”.
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Imbimbo, C., Rovere, D. & Warman, A. Superconformal anomalies from superconformal Chern-Simons polynomials. J. High Energ. Phys. 2024, 277 (2024). https://doi.org/10.1007/JHEP05(2024)277
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DOI: https://doi.org/10.1007/JHEP05(2024)277