DOI: 10.1007/jhep08(2026)043 ISSN: 1029-8479
Superconformal weight shifting operators
Tobias Hansen, Paul Heslop, Hector Puerta-Ramisa
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.