Title:

Improvements in the largeNc approximation

In the first two chapters we present a review of the largeNc approximation, outlining its status within quantum field theory, and presenting the main formalisms that are used. We compare them, and note a number of problems with the results that are obtained. We then look at the resolution of these problems for the remainder of the thesis. In the third chapter we examine two different largeNc techniques: effective lagrangians and chiral soliton models. There are many apparent discrepancies between the two techniques. Building upon previous work by Dorey, Hughes and Mattis, we show how these discrepancies can be resolved in a number of simple cases. Starting from an effective theory, the leading order diagrams contributing to a physical process contain divergent loop integrals over meson momenta, hence it is necessary to impose an explicit ultraviolet cutoff on the theory. We analyse the effective models by examining the first few terms in an expansion of the meson sector of the theory, in terms of derivatives on the meson fields. In our analysis, we were particularly interested in examining the flow of the theory, under the action of the largeNc renormalization group. We looked at the effects of massive pions and higher derivative terms on this flow. In particular, we looked for the circumstances under which the flow could be followed to the continuum limit. We present a counterexample to the conjecture of Dorey et al., and discover that it is possible to obtain a nonsolitonic continuum limit. We investigated the 'universality' of the largeNc renormalization group, in particular against a variation in the type of cutoff used. Then we looked at how the largeNc renormalization group could be used to obtain phenomenological nucleon models, which include the chiral soliton models as a special class. We found that these models could improve upon the Skyrme model, by solving some of the difficulties noted previously. In the fourth chapter we look at the disagreement between the largeNc approximation and chiral perturbation theory over certain quantities. We review the sources of these discrepancies in the two limits, and find that the real world can be considered to lie between them. Following work by Cohen, we combined the two limits by doing the calculations whilst holding MπNc fixed. We show how the resulting chiral large Nc calculations improve upon the large. Nc approximation by including the effects of baryon rotation, resolving the disagreement between the two separate limits. In particular we calculate the nonanalytic contribution to the nucleon mass and the isovector charge radius, and show that the correct forms for the chiral largeNc behaviour can be obtained just by using semiclassical techniques. Finally, we investigate how rotational effects can be included in the Skyrme model. We propose a form for the rotationally improved Skyrmion, and analyse some of its properties.
