The naive quark model has been remarkably successful in classifying the many hadron states so far discovered. The underlying theory for these successes is QCD. This theory, however, not only suggests states made purely of quarks, but also those containing glue. Whether these pure glue states are observable depends on the validity of the notion of valence gluons which has been explored in the earlier part of this thesis. My studies show that the hard and soft gluon components can be distinguished and behave as valence and sea constituents in glueballs. These glueballs, and especially the ground state, must be found in order to establish QCD as a successful theory of strong interactions. Because of the inevitability of mixing, particularly for low mass states, simple parton configurations cannot be expected in practice, so supposedly characteristic decay patterns may not serve as a guide to the existence of new states. The only reliable way to establish the intrusion of extra dynamics is to count the number of states with given quantum numbers. An extensive coupled channel analysis of results on ππ and KK final states interactions with I≈0 0(^++) quantum numbers below 1.7 GeV has been performed incorporating new data on pp ÷ pp ππ(KK), Though no poles are imposed on these data, we find that 3 distinct resonances emerge in the 1 GeV region, when the naive quark model requires but two. This clearly indicates for the first time definite evidence for dynamics beyond the quark model in the 0(^++) channel. Our results are consistent with the presence of the ground state glueball S(_1)(993) together with ideally mixed quark model states S(_2)(988) and ε(900).

The first part of this work gives a general background for the ideas involved in the research presented in this thesis. Coupling constants, Renor-malisation Group Equation, Grand Unified Theories (GUTs) and Super symmetry (SUSY) are briefly introduced. Following this, we analyse the unification parameters M(_GUT) and l/α(_GUT) as functions of the number of fermion families (F) and Higgs boson multiplets (S). Analytical and numerical solutions to the leading and next-to-leading order evolution equation for the couplings a, are obtained. This is done in the context of the Standard Model embedded in SU(5), SUSY SU(5) and L-R SO(IO). In all these GUTs, the first order analytical approach proves itself a useful probe to examine the structure of M(_GUT) and l/α(_GUT) in terms of the variables F and S. General trends remain the same after including second order corrections to the evolution equations. Recent precision data for the coupling constants allow more definitive conclusions to be reached. We find that restrictions on the unification parameters constrain F and S in such a way that SU(5) is ruled out by constraints on 5 (in agreement with previous results), F is severely limited in SUSY SU(5) and, unlike SUSY SU(5), an acceptable unification scenario can still be obtained when Higgs bosons are ignored in L-R SO(IO). The structures of the latter two GUTs are found to be very different although some features are common to both.

We examine the use of branes as probes of supergravity geometries which arise in the study of gauge theory/gravity dualities. We investigate the moduh spaces of supersymmetric gauge theories through moduh spaces of brane probes in the dual gravity theories. Preferred coordinate systems emerge in which the supergravity geometries can readily be compared to the gauge theory and various gauge theory quantities such as anomalous scaling dimensions can be read off. We also consider the physics of certain expanded brane configurations, called giant gravitons. We identify supergravity solutions which represent coherent states of these objects. We find a degeneracy between giant graviton probes and massless particles in a broad class of supergravity backgrounds and uncover a close relationship with charged particle states in lower dimensions.

In this thesis we compute characters and supercharacters of irreducible admissible representations for the two affine superalgebras osp(l,2;C) and l(2|l;C).The work on osp(l, 2; C) includes a derivation of the embedding diagram. We compute the modular transformations of the Neveu-Schwarz characters of osp(l, 2; C) and show that they transform in a manner consistent with the different possible free fermion spin structures on a torus. In chapter 3 we turn our attention to ŝl(2|l;C). Characters and supercharacters are computed for three classes of admissible representation. We have to derive the embedding diagram for one of these classes. We show that the integrable characters in the classes we study are identical to characters of the N = 4 superconformal algebra and that some of the sl(2|l;C) characters have a pole in a certain limit. The residue at this pole is computed and it is found to be proportional to an N = 2 minimal character. Specialising to fractional levels k of the form k + 1 = l/u,u ϵ N, we consider the SL(2|1)/SL{2) coset theory and make a conjecture that it is a product of a parafermion theory and a rational torus model. The appearance of parafermion characters and rational torus model characters in the branching functions of some examples that we have worked out leads to a conjecture for the general form of the branching functions whenever the level k has the form k + 1 = 1/u.The modular T transformation can be worked out easily for any character or super- character we have computed. We work out the 5 transformation of the Neveu-Schwarz characters in two examples and find that we get a unitary S-matrix in each case. The thesis finishes with some interesting identities between ŝu(2) string functions which are a corollary of the work on branching functions.

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The enhancon mechanism is a specific phenomenon in string theory which resolves a certain naked spacetime singularity arising in the supergravity description related to N = 2 supersymmetric pure gauge theory. After reviewing the problem of singularities in general relativity as well as in string theory, and discussing the prototypical enhancon example constructed by wrapping D6-branes on a K3 surface, the thesis presents three generalisations to this static spherically symmetric case pertaining to large N SU{N) gauge theory. First we will use orientifolds to show how the enhancon mechanism also works in similar situations related to SO(2N + 1), USp(2N) and SO{2N) gauge theories. Second we will wrap D-brane distributions on K3 to obtain the enhancon in oblate, toroidal and prolate shapes. Third we will study a rotating enhancon configuration and consider its implications for the black hole entropy and the second law of thermodynamics.

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In this thesis we present techniques for the calculation of two-loop integrals contributing to the virtual corrections to physical processes with three on-shell and one-off-shell external particles. First, we describe a set of basic tools that simplifyy the manipulation of complicated two-loop integrals. A technique for deriving helicity amplitudes with use of a set of projectors is demonstrated. Then we present an algorithm, introduced by Laporta, that helps reduce all possible two-loop integrals to a basic set of 'master integrals'. Subsequently, these master integrals are analytically evaluated by deriving and solving differential equations on the external scales of the process. Two-loop matrix elements and helicity amplitudes are calculated for the physical processes γ* → qqg and H → ggg respectively. Conventional Dimensional Regularization is used in the evaluation of Feynman diagrams. For both processes, the infrared singular behaviour is shown to agree with the one predicted by Catani.

Motivated by recent observations suggesting that structures in the Universe appear to be concentrated on the walls of bubbles that surround giant voids, we examine the possibility that the observed structure may have resulted from a first order phase transition that occured after inflation and which proceeded by quantum tunnelling and the formation of bubbles of true vacuum. Since we lack a fundamental theory of particle physics that would define the scalar field responsible for the second phase change and predict the scale of the resulting structures, we instead examine two similar parametrised forms for the potential motivated by the standard Higgs model, and attempt to determine values of the parameters that can reproduce the kind of structures that are observed through bubble wall collisions. The method deployed is quite general and can be applied to any phase transition that occured after inflation. It is found that although the shape of the required potential and its coupling can be determined, the epoch of the proposed second phase transition is in general not specified by the observed structures. The full verification or otherwise of our proposal will require not only a more detailed consideration of its predictions for the large scale structure of the Universe and its compatibility with the cosmic microwave background radiation but also the embedding of our ideas in a credible theory of particle physics beyond the Standard Model.