Superconformal Weight Shifting Operators

Tobias Hansen; Paul Heslop; Hector Puerta-Ramisa

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arXiv · 2506.08682

Superconformal Weight Shifting Operators

Tobias Hansen·Paul Heslop·Hector Puerta-Ramisa

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Abstract

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.

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Tobias Hansen, Paul Heslop, Hector Puerta-Ramisa. 2025-06-10. Superconformal Weight Shifting Operators. https://arxiv.org/abs/2506.08682

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