The Superconformal Xing Equation

TL;DR

This paper develops a mathematical framework to formulate crossing symmetry equations for four-point functions in all 4D superconformal field theories, enabling non-perturbative analysis of their dynamics.

Contribution

It introduces a supergroup theoretic method for constructing tensor structures, generalizing previous approaches to include all 4D superconformal theories.

Findings

Derived crossing symmetry constraints for long multiplet four-point functions.

Unified formalism applicable to all 4D superconformal field theories.

Enhanced tools for non-perturbative studies of superconformal dynamics.

Abstract

Crossing symmetry provides a powerful tool to access the non-perturbative dynamics of conformal and superconformal field theories. Here we develop the mathematical formalism that allows to construct the crossing equations for arbitrary four-point functions in theories with superconformal symmetry of type I, including all superconformal field theories in $d=4$ dimensions. Our advance relies on a supergroup theoretic construction of tensor structures that generalizes an approach which was put forward in \cite{Buric:2019dfk} for bosonic theories. When combined with our recent construction of the relevant superblocks, we are able to derive the crossing symmetry constraint in particular for four-point functions of arbitrary long multiplets in all 4-dimensional superconformal field theories.