On perturbative field theory and twistor string theory

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.

123+56 pages, 29 figures, uses axodraw.sty; PhD thesis. v3: Reference added, appendix updated

References in corpus (17)

• Three-Loop Superfiniteness of N=8 Supergravity
• From Twistor Actions to MHV Diagrams
• Tree Level Recursion Relations In General Relativity
• N=2 strings and the twistorial Calabi-Yau
• Holomorphic Anomaly Of Unitarity Cuts And One-Loop Gauge Theory Amplitudes
• Mirror Symmetry and Supermanifolds
• Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
• A mini-course on topological strings
• Super-Chern-Simons Theory as Superstring Theory
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS
• Twistor diagram recursion for all gauge-theoretic tree amplitudes
• A quantization of twistor Yang-Mills theory through the background field method
• Self-Dual Supergravity and Twistor Theory
• Sigma Models with N=8 Supersymmetries in 2+1 and 1+1 Dimensions
• One-loop N=8 Supergravity Amplitudes from MHV Diagrams
• Notes on One-loop Calculations in Light-cone Gauge
• String Theories on Flat Supermanifolds