Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations

Understand

In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in $\mathcal{N}=4$ super Yang-Mills theory at various loop orders and for various numbers of external legs.

• We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result.
• We also investigate the properties of the corresponding remainder functions.
• Moreover, we extend on-shell diagrams, a Gra{\ss}mannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of the stress-tensor supermultiplet as an example.