On perturbative field theory and twistor string theory

TL;DR

This paper explores the simplicity of scattering amplitude calculations in field theory and twistor string theory, introducing new computational techniques and results for gauge and gravity theories relevant to high-energy physics.

Contribution

It presents new amplitude calculations in QCD and gravity, reviews twistor string techniques, and introduces recursive methods for perturbative gravity analysis.

Findings

Verified one-loop gluonic MHV amplitudes in N=1 super-Yang-Mills

Calculated new MHV amplitudes in pure Yang-Mills with scalar loops

Derived a new compact form for n-graviton MHV amplitudes

Abstract

It is well-known that perturbative calculations in field theory can lead to far simpler answers than the Feynman diagram approach might suggest. In some cases scattering amplitudes can be constructed for processes with any desired number of external legs yielding compact expressions which are inaccessible from the point of view of conventional perturbation theory. In this thesis we discuss some attempts to address the nature of this underlying simplicity and then use the results to calculate some previously unknown amplitudes of interest. Witten's twistor string theory is introduced and the CSW rules at tree-level and one-loop are described. We use these techniques to calculate the one-loop gluonic MHV amplitudes in N=1 super-Yang-Mills as a verification of their validity and then proceed to evaluate the general MHV amplitudes in pure Yang-Mills with a scalar running in the loop. This latter amplitude is a new result in QCD. In addition to this, we review some recent on-shell recursion relations for tree-level amplitudes in gauge theory and apply them to gravity. As a result we present a new compact form for the n-graviton MHV amplitudes in general relativity. The techniques and results discussed are relevant to the understanding of the structure of field theory and gravity and the non-supersymmetric Yang-Mills amplitudes in-particular are pertinent to background processes at the LHC. The gravitational recursion relations provide new techniques for perturbative gravity and have some bearing on the ultraviolet properties of Einstein gravity.