Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
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| Format: | Preprint |
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2024
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| author | Buchbinder, Evgeny I. Hutomo, Jessica Stone, Benjamin J. |
| author_facet | Buchbinder, Evgeny I. Hutomo, Jessica Stone, Benjamin J. |
| contents | We analyse the general structure of the three-point functions involving conserved higher-spin ``vector-like" supercurrents $J_{s}(z) := J_{α(s) \dotα(s)}(z)$ in four-dimensional $\mathcal{N}=1$ superconformal field theory. Using the constraints of superconformal symmetry and superfield conservation equations, we utilise a computational approach to analyse the general structure of the three-point function $\langle J^{}_{s_{1}}(z_{1}) \, J'_{s_{2}}(z_{2}) \, J''_{s_{3}}(z_{3}) \rangle$ and provide a general classification of the results. We demonstrate that the three-point function is fixed up to $2 \min (s_{i}) + 2$ independent conserved structures, which we propose to hold for arbitrary superspins. In addition, we show that the conserved structures can be classified as parity-even or parity-odd in superspace based on their transformation properties under superinversion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_17106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins Buchbinder, Evgeny I. Hutomo, Jessica Stone, Benjamin J. High Energy Physics - Theory Mathematical Physics We analyse the general structure of the three-point functions involving conserved higher-spin ``vector-like" supercurrents $J_{s}(z) := J_{α(s) \dotα(s)}(z)$ in four-dimensional $\mathcal{N}=1$ superconformal field theory. Using the constraints of superconformal symmetry and superfield conservation equations, we utilise a computational approach to analyse the general structure of the three-point function $\langle J^{}_{s_{1}}(z_{1}) \, J'_{s_{2}}(z_{2}) \, J''_{s_{3}}(z_{3}) \rangle$ and provide a general classification of the results. We demonstrate that the three-point function is fixed up to $2 \min (s_{i}) + 2$ independent conserved structures, which we propose to hold for arbitrary superspins. In addition, we show that the conserved structures can be classified as parity-even or parity-odd in superspace based on their transformation properties under superinversion. |
| title | Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.17106 |