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arXiv · 2311.05684

Superconformal anomalies from superconformal Chern-Simons polynomials

Camillo Imbimbo·Davide Rovere·Alison Warman
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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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Camillo Imbimbo, Davide Rovere, Alison Warman. 2023-11-09. Superconformal anomalies from superconformal Chern-Simons polynomials. https://doi.org/10.1007/jhep05(2024)277

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