The superconformal equation

• Main Authors: Ilija Burić, Volker Schomerus, Evgeny Sobko
• Format: Article
• Language: English
• Published: SpringerOpen 2020-10-01
• Series: Journal of High Energy Physics
• Subjects: Conformal and W Symmetry; Conformal Field Theory; Field Theories in Higher Dimensions; Superspaces
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2020)147

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 the- ories in d = 4 dimensions. Our advance relies on a supergroup theoretic construction of tensor structures that generalizes an approach which was put forward in [1] 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.