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Efficient techniques for calculating scattering amplitudes in non-abelian gauge theories. / Steven James Bidder

Swansea University Author: Steven James Bidder

Abstract

Recently, a duality between = 4 Super Yang-Mills Theory and Twistor String Theory has been proposed by Witten [1]. This has led to the development of a number of new techniques for calculating Tree and Loop scattering amplitudes in theories with N = A Supersymmetries. In this thesis we examine how t...

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Published: 2006
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42501
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Abstract: Recently, a duality between = 4 Super Yang-Mills Theory and Twistor String Theory has been proposed by Witten [1]. This has led to the development of a number of new techniques for calculating Tree and Loop scattering amplitudes in theories with N = A Supersymmetries. In this thesis we examine how these techniques can be extended to calculate purely gluonic one-loop scattering amplitudes in theories with & 4 Supersymmetries. We explicitly calculate six-point N = 1 next to MHV (NHMV) one-loop amplitudes, and certain n-point NMHV examples, and investigate their twistor structure. We find that the box coefficients of all Supersymmetric amplitudes inherit the same Twistor Space properties, but that the Twistor description does not extend to the coefficients of the Triangle and Bubble functions that also appear in amplitudes in theories with N & 4 Supersymmetries. We also show how to use Supersymmetric Ward Identities to calculate amplitudes involving external fermions and scalars from the known purely gluonic amplitudes with the same helicity structure. We present explicit results for six-point N = 4 NMHV one-loop amplitudes and generalise these results to n-point amplitudes, presenting the full generalisation as a series of conversion factors that take amplitudes from the purely gluonic form to the case where there are two external fermions. Finally we discuss how these factors can then be compounded to give amplitudes with more external fermions and scalars.
Keywords: Theoretical physics.
College: College of Science