Bootstrapping SCFTs with four supercharges

Abstract

We study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension 2 ≤ d ≤ 4. We show how superconformal algebras with four Poincaré supercharges can be treated in a formalism applicable to any, in principle continuous, value of d and use this to construct the superconformal blocks for any d ≤ 4. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the d = 2, $$ \mathcal{N}=\left(2,\;2\right) $$ minimal model with central charge c = 1 and the theory of a free chiral multiplet in d = 4, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.