2025/06/10 by Tobias Hansen, Hansen, Tobias, Paul Heslop +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2506.08682
openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a framework for constructing superconformal blocks for correlators of general supermultiplets in theories with SU(m,m|2n) symmetry, such as four-dimensional N=2 and N = 4 conformal theories. We use analytic superspace, viewed as the super-Grassmannian 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 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.