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Self interaction of gluons within the M.I.T. bag model
(1990) Quick, Jonathan Francis Hare
One consequence of the non-abelian nature of Quantum Chromodynamic ( QCD ) gauge theory is that its gauge particles, or gluons as they are called, must be able to interact with each other. It has long been suggested that this must give rise to a complicated QCD vacuum structure, and many attempts to describe and model such a. problem can be found in the literature. Another consequence of the self-interaction or "be gluons is the effect of colour confinement, which specifies that. only colour-charge neutral objects may exist in, free space. One of the most successful models in QCD so far takes into account this confinement effect directly, by means of a phenomenological confining potential or bag. The aim of this thesis is to consider the structure ot the QCD vacuum within the confines of such a bag. (Abbreviation abstract)
Investigation of higher spin theory through holography and mathematical methods in free conformal field theory
(2017) Rabe, Randle
In this dissertation, we will develop novel methods for determining the spectrum of primary operators in a free conformal eld theory (vector model) and to construct some of these primaries. To count the spectrum of primaries, we use group theoretic techniques to obtain character formulas for any number of elds as representations of SO(4; 2). More precisely, we will construct generating functions that can be expanded to any order in the conformal scaling dimension to yield the complete spectrum of primaries constructed out of n scalar elds. We also develop e cient methods to construct these primaries by using a polynomial description. Finally, these primary operators, which are higher spin currents in the free conformal vector model, correspond to higher spin gauge elds in Vasiliev higher spin theory through the holographic duality.
Large N conformal field theory from gauge/gravity duality
(2017) Hasina Tahiridimbisoa, Nirina Maurice
In this dissertation we exploit the Ads slash CFT correspondence to describe a system of strings suspended between giant gravitons. The strings can be in an excited state. The excitations of the strings can be given a particle-like description and are known as magnons. The proposed gauge invariant operators used to construct a complete description of this system belong to the su(2) sector of the N = 4 SYM. Using an open spin chain description of the suspended strings, the states of the system we consider enjoy an SU 2j2)2 symmetry. By making use of this symmetry, we compute the all loop anomalous dimensions of these operators. The spectrum of the dilatation operator in the su(2) sector of the theory is reproduced in the dual gravity description. In the dual theory, the energies of the magnons are computed using strings in a background LLM geometry and the results are in complete agreement with the anomalous dimensions of the operators we have considered. Using the symmetries enjoyed by our system we achieve a complete determination - up to an overall phase - of the reection/scattering matrix between a boundary magnon and a bulk magnon. Thus, although the open boundary conditions of the spin chain spoil integrability. The two-loop subleading correction to the dilatation operator is also explored. This subleading term corresponds to a correction of the magnon energies. The computation of this subleading term requires consideration of the giant's backreaction on their excitations. We nd that this backreaction implies a nontrivial mixing of the dual operators and this mixing is characterized completely.
Gauge gravity dualities at finite N
(2014-07-30) Mabanga, Wandile
In this dissertation we compute the anomalous dimensions for a class of operators, belonging to the SU(3) sector of the theory, that have a bare dimension of order N. For these operators the large N limit and the planar limit are distinct and summing only the planar diagrams will not capture the large N dynamics. Although the spectrum of anomalous dimensions has been computed for this class of operators, previous studies have neglected certain terms which were argued to be small. After dropping these terms diagonalizing the dilatation operator reduces to diagonalizing a set of decoupled oscillators. In this dissertation we explicitely compute the terms which were neglected previously and show that diagonalizing the dilatation operator still reduces to diagonalizing a set of decoupled oscillators.
Non-planar Ads/CFT from group representation theory
(2014-06-12) Smith, Stephanie
In this thesis we explore certain limits of the AdS/CFT correspondence for integrability. This is done by calculating the action of the dilatation operator on operators known as restricted Schur polynomials, which are AdS/CFT dual to D3-branes known as giant gravitons. We focus on operators in N = 4 super-Yang-Mills theory, which is dual to type IIB string theory on an AdS5×S5 background. We find that, in various cases, this theory is integrable in a large N non-planar limit.

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