Dr Giulio Gambuti

Abstract:

We consider the harmonic gauge condition in linearized gravity, seen as a gauge theory for a symmetric tensor field. Once the harmonic gauge condition is implemented, as customary, according to the Faddeev-Popov procedure, the gauge fixed action still depends on one gauge parameter. Consequently, the harmonic gauge appears to be a class of conditions, rather than a particular one. This allows to give a physical motivation for the covariant harmonic gauge(s), which emerges when the gravitational perturbation is given a mass term. In fact, for a particular choice of harmonic gauge, we find a theory of linearized massive gravity displaying five degrees of freedom, as it should, and which is not affected by the vDVZ discontinuity, differently from what happens in the standard Fierz-Pauli theory.

Abstract:

Scattering amplitudes provide insight into the all-orders structure of gauge theories. Particularly rich is their non-planar sector, where new and interesting physical phenomena appear. This thesis aims to push the boundaries of perturbative scattering amplitudes, with special emphasis on calculations in massless Quantum Chromodynamics. We review the colour and helicity decomposition of gauge theory amplitudes, as well as the structure of their ultraviolet and infrared divergences. We then discuss the application of state-of-the-art methods to the computation of all four-point three-loop scattering amplitudes in Quantum Chromodynamics. As an immediate consequence we both verify the structure of infrared divergences and extract the gluon Regge trajectory at the corresponding perturbative order. We further describe the computation of five-gluon scattering at the two-loop order, with special emphasis on the multi-scale complexity of this process. Finally, we explore the idea of simplifying the integrand representation of gauge theoretic scattering amplitudes by leveraging their highly-constrained infrared structure. We provide a proof-of-concept application to two-loop four- gluon scattering amplitudes.