The Superconformal Xing Equation

Understand

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.