Long Multiplet Bootstrap

Abstract: Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained form correlation functions of very special fields in short (BPS) representations of the superconformal algebra. Our main goal is to initiate a superconformal bootstrap for long multiplets, one that exploits all constraints from superprimaries and their descendants. To this end, we work out the Casimir equations for four-point correlators of long multiplets of the two-dimensional global $\mathcal{N}=2$ superconformal algebra. After constructing the full set of conformal blocks we discuss two different applications. The first one concerns two-dimensional (2,0) theories. The numerical bootstrap analysis we perform serves a twofold purpose, as a feasibility study of our long multiplet bootstrap and also as an exploration of (2,0) theories. A second line of applications is directed towards four-dimensional $\mathcal{N}=3$ SCFTs. In this context, our results imply a new bound $c \geqslant \tfrac{13}{24}$ for the central charge of such models, which we argue cannot be saturated by an interacting SCFT.