Form factors in superconformal theories in four and three dimensions

Abstract

This thesis focuses on form factors in superconformal theories, in particular maximally supersymmetric Yang-Mills (MSYM) and ABJM. Scattering amplitudes in these theories have a wealth of special properties and significant amount of insight has been developed for these along with the modern techniques to calculate them. In this thesis, it is presented that form factors have very similar properties to scattering amplitudes and the techniques for scattering amplitudes can be successfully applied to form factors. After a review of the methods employed, the results for tree-level and multi-loop form factors of protected operators are derived. In four dimensions, it is shown that the tree-level form factors can be computed using MHV diagrams BCFWrelations by augmenting the set of vertices with elementary form factors. Tree and loop-level MHV and non-MHV form factors of protected operators in the stress-tensor multiplet of MSYM are computed as examples. A solution to the BCFW recursion relations for form factors is derived in terms of a diagrammatic representation. Supersymmetric multiplets of form factors of protected operators are constructed. In three dimensions, Sudakov form factor of a protected biscalar operator is computed in ABJM theory. This form factor captures the IR divergences of the scattering amplitudes. It is found that this form factor can be written in terms of a single, non-planar Feynman integral which is maximally transcendental. Additionally, the sub-leading colour corrections to the one-loop four-particle amplitude in ABJM is derived using unitarity cuts. Finally a basis of two-loo pure master integrals for the Sudakov form factor topology is constructed from a principle that relies on certain unitarity cuts.