On multipoint Ward identities for superconformal line defects

TL;DR

This paper derives superconformal Ward identities for multipoint correlators of topological operators on line defects, providing a universal and simplified approach that is validated through examples in 4d super Yang-Mills theory.

Contribution

It introduces a universal method to derive superconformal Ward identities for multipoint correlators on line defects, connecting topological constraints with known identities.

Findings

Correlators become topological after a twist, simplifying analysis.

Topological constraints refine correlator behavior beyond the topological limit.

Derived Ward identities match known results for 4-point functions and are illustrated in 4d super Yang-Mills.

Abstract

Superconformal Ward identities are revisited in the context of superconformal line defects. Multipoint correlators of topological operators inserted on superconformal lines are studied. In particular, it is known that protected operators preserving enough of the supersymmetry become topological after performing a topological twist. By definition, such a correlator is constant in the topological limit. By analysing the topological constraint on the OPE of such operators, the correlator is further constrained away from this limit. The constraints on multipoint correlators match the known superconformal Ward identities in the case of 4-point functions. This allows for an simple and universal derivation of the superconformal Ward identities governing the multipoint correlation functions of such operators. This concept is illustrated by 1/2-BPS operators with an $su(2)$ R-symmetry and further explored in the case of the displacement multiplet on the 1/2-BPS Wilson line in 4d $\mathcal{N}=4$ super Yang-Mills theory supporting the conjectured multipoint Ward identities in the literature.