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Title: Ultra-violet infinities and counterterms in higher dimensional Yang-Mills and gravity
Author: Turner, N. W. P.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2003
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Theories which have a dimensional coupling constant are generally considered non-renormalisable unless the loop diagrams are free of ultra-violet divergences. In this work we investigate two theories in higher dimensions which have (positive) dimensionful coupling constants; Yang-Mills theory and gravity. We calculate the ultra-violet infinities associated with the one-loop four-point on-shell amplitudes using two methods which are more efficient than a Feynman diagram approach, these are the Cutkosky cutting technique and the Bern-Kosower string based rules. Dimensional regularisation is used to regulate the integrals and so the infinities only appear in even dimensions (at one-loop). Different particle types are considered circulating within the loop and the counterterms necessary to render these theories one-loop finite are determined for different dimensions. For the Yang-Mills case, we calculate the infinities associated with one-loop amplitudes with external gluons and consider scalars, fermions and gluons within the loop. These are determined for six, eight and ten dimensions and we find that supersymmetric combinations within the loop do, in general, simplify the counterterm structure and for six dimensions the counterterm vanishes. For gravity in six dimensions we consider one-loop amplitudes with combinations of external gravitons and two-forms and extract the infinities of these. We find that again in six dimensions and counterterm for supersymmetric matter within the loop is zero. In eight dimensions we investigate one-loop amplitudes with external gravitons and determine the counterterm structure for various particles within the loop. Supersymmetry does simplify the counterterm structure, but they do not vanish. We have also included more one-loop amplitudes than are necessary to determine the counterterms in order to provide a database for others.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available