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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2506.08682 |
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| _version_ | 1866915999369920512 |
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| author | Hansen, Tobias Heslop, Paul Puerta-Ramisa, Hector |
| author_facet | Hansen, Tobias Heslop, Paul Puerta-Ramisa, Hector |
| contents | We develop a framework for constructing superconformal blocks for correlators of general supermultiplets in theories with $\mathrm{SU}(m,m|2n)$ symmetry, such as four-dimensional $\mathcal{N}=2$ and $\mathcal{N} = 4$ conformal theories. We use analytic superspace, viewed as the super-Grassmannian $\mathrm{Gr}(m|n,2m|2n)$, which includes 4D Minkowski space ($m=2,n=0$). In this formalism, superblocks for non-half-BPS correlators are analogous to non-supersymmetric conformal blocks for correlators of fields with spin. We construct $\mathrm{SU}(m,m|2n)$-covariant differential operators which generalise the existing conformal weight-shifting operators, and thus allow us to derive all superconformal blocks from the known half-BPS blocks. Our results provide a framework from which to advance the conformal bootstrap in 4D supersymmetric settings, with potential extensions to lower and higher-dimensional SCFTs. The Grassmannian formalism is also seen to offer a natural and often simpler alternative to the embedding space formalism of non-supersymmetric CFTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08682 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superconformal Weight Shifting Operators Hansen, Tobias Heslop, Paul Puerta-Ramisa, Hector High Energy Physics - Theory Mathematical Physics We develop a framework for constructing superconformal blocks for correlators of general supermultiplets in theories with $\mathrm{SU}(m,m|2n)$ symmetry, such as four-dimensional $\mathcal{N}=2$ and $\mathcal{N} = 4$ conformal theories. We use analytic superspace, viewed as the super-Grassmannian $\mathrm{Gr}(m|n,2m|2n)$, which includes 4D Minkowski space ($m=2,n=0$). In this formalism, superblocks for non-half-BPS correlators are analogous to non-supersymmetric conformal blocks for correlators of fields with spin. We construct $\mathrm{SU}(m,m|2n)$-covariant differential operators which generalise the existing conformal weight-shifting operators, and thus allow us to derive all superconformal blocks from the known half-BPS blocks. Our results provide a framework from which to advance the conformal bootstrap in 4D supersymmetric settings, with potential extensions to lower and higher-dimensional SCFTs. The Grassmannian formalism is also seen to offer a natural and often simpler alternative to the embedding space formalism of non-supersymmetric CFTs. |
| title | Superconformal Weight Shifting Operators |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.08682 |