The ${\mathcal N}=2$ superconformal bootstrap

TL;DR

This paper initiates the conformal bootstrap program for four-dimensional ${\mathcal N}=2$ superconformal field theories, providing a unified operator-algebraic framework and deriving constraints on operator data through numerical analysis.

Contribution

It introduces a unified operator-algebraic approach for ${\mathcal N}=2$ theories and formulates conjectures about their landscape, along with detailed analysis of four-point functions and superconformal blocks.

Findings

Derived constraints on operator dimensions and OPE coefficients.

Solved superconformal Ward identities for key correlators.

Established a foundation for numerical bootstrap studies of ${\mathcal N}=2$ theories.

Abstract

In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of ${\mathcal N}=2$ chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any ${\mathcal N}=2$ superconformal field theory.