Superconformal anomalies from superconformal Chern-Simons polynomials
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929364973649920 |
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| author | Imbimbo, Camillo Rovere, Davide Warman, Alison |
| author_facet | Imbimbo, Camillo Rovere, Davide Warman, Alison |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05684 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Superconformal anomalies from superconformal Chern-Simons polynomials Imbimbo, Camillo Rovere, Davide Warman, Alison High Energy Physics - Theory 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. |
| title | Superconformal anomalies from superconformal Chern-Simons polynomials |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.05684 |