Scattering amplitudes in gauge theories with and without supersymmetry

TL;DR

This thesis advances the understanding of perturbative gauge theory amplitudes by analyzing recursion relations, computing one-loop gluon amplitudes in supersymmetric theories, and exploring the color-kinematic duality extending to fundamental particles.

Contribution

It introduces conditions for valid recursion relations in off-shell Yang-Mills theory, rederives spinor integration for amplitude coefficients, and extends BCJ duality to include fundamental particles.

Findings

Recursion relations avoid unphysical poles under certain conditions.

Analytic computation of one-loop gluon amplitudes in N=1 super-Yang-Mills.

Extension of BCJ duality to fundamental representation particles.

Abstract

This thesis aims at providing better understanding of the perturbative expansion of gauge theories with and without supersymmetry. At tree level, the BCFW recursion relations are analyzed with respect to their validity for general off-shell objects in Yang-Mills theory, which is a significant step away from their established zone of applicability. Unphysical poles constitute a new potential problem in addition to the boundary behavior issue, common to the on-shell case as well. For an infinite family of massive fermion currents, both obstacles are shown to be avoided under the certain conditions, which provides a natural recursion relation. At one loop, scattering amplitudes can be calculated from unitarity cuts through their expansion into known scalar integrals with free coefficients. A powerful method to obtain these coefficients, namely spinor integration, is discussed and rederived in a somewhat novel form. It is then used to compute analytically the infinite series of one-loop gluon amplitudes in N = 1 super-Yang-Mills theory with exactly three negative helicities. The final part of this thesis concerns the intriguing relationship between gluon and graviton scattering amplitudes, which involves a beautiful duality between the color and kinematic content of gauge theories. This BCJ duality is extended to include particles in the fundamental representation of the gauge group, which is shown to relieve the restriction of the BCJ construction to factorizable gravities and thus give access to amplitudes in generic (super-)gravity theories.