Constraints from Superconformal Symmetry on Higher Point Functions

This thesis investigates the superconformal Ward identities (SCWI) for higher point correlation functions within the maximally symmetric four-dimensional superconformal field theory of N = 4 Super Yang-Mills (SYM) theory. As a cornerstone of theoretical physics, N = 4 SYM is notable for its high degree of symmetry, properties of integrability, and its duality through the AdS/CFT correspondence, providing remarkable insights also into strongly coupled physics. The constraints imposed by SCWI are essential for understanding the behavior of key objects in this theory. Studying SCWI for higher points, particularly five-point functions and beyond, is crucial for extracting additional conformal field theory (CFT) data via the bootstrap program and for gaining deeper understandings of phenomena such as integrability, hidden symmetries and the AdS/CFT correspondence. This work develops a systematic method utilising analytic superspace to derive these higher point superconformal Ward identities for half-BPS multiplets. Although exemplified through stress-tensor multiplets, the method is adaptable and applicable to various superconformal setups. In particular, it is designed to work independently of the number of inserted operators, addressing limitations of previous techniques used for lower-point functions. To further illustrate the adaptability of our approach, we also apply it to the six-point function of displacement multiplets on the supersymmetric Wilson line defect in N = 4 SYM.