Superconformal weight shifting operators

A bstract We develop a framework for constructing superconformal blocks for correlators of general supermultiplets in theories with SU( m , m |2 n ) symmetry, such as four-dimensional $$ \mathcal{N} $$ N = 2 and $$ \mathcal{N} $$ N = 4 conformal theories. We use analytic superspace, viewed as the super-Grassmannian Gr( m | n , 2 m |2 n ), 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 |2 n )-covariant differential operators which generalise the existing conformal weight-shifting operators, and thus allow us to derive non half-BPS 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.