In this Thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. We propose first a model to re-write the Faddeev-Popov quantisation method in terms of grouptheoretical techniques and then we give a possible way to solve the no-go theorem of ...

Image compression is concerned with reducing the amount of data needed to represent an image. Efficient image representation is achieved by exploiting the statistical and psychovisual redundancies of an image. This reported focusses on the main principles of information theory, which provides a framework for efficient signal coding from a statistical perspective. Two of the fundamental theories...

Whilst supergravity theories go a certain way to tame the infinities of their non-supersymmetric cousins, they also generalise these theories by coupling fermionic degrees of freedom to the original gravity theory. One can easily see this at the continuum classical level. We want to investigate this issue in the discrete quantum case. Thus, in this paper, we shall analyze a rather simplified mo...

We study the dynamics of BPS D3–branes wrapped on a three–sphere in AdS5× L, so–called dual giant gravitons, where L is a Sasakian five–manifold. The phase space of these configurations is the symplectic cone X over L, and geometric quantisation naturally produces a Hilbert space of L2–normalisable holomorphic functions on X, whose states are dual to scalar chiral BPS operators in the dual supe...

The temperature dependence of quantum Hall conductivities is studied in the context AdS/CMT paradigm using a model with bulk theory consisting (3+1)-dimensional Einstein-Maxwell action coupled to dilaton and an axion, negative cosmological constant. We consider solution which has Lifshitz like geometry dyonic black-brane bulk. There $Sl(2,R)$ corresponding electromagnetic duality, maps between ...

We consider the geometric quantisation of Chern--Simons theory for closed genus-one surfaces and semisimple complex groups. First we introduce natural complexified analogue Hitchin connection in K\{a}hler quantisation, with polarisations coming from nonabelian Hodge hyper-K\{a}hler geometry moduli spaces flat connections, thereby complementing real-polarised approach Witten. Then Witten, identi...

In this work we study the quantisation of Seiberg-Witten curve for E-string theory compactified on a two-torus. We find that resulting operator expression belongs to class elliptic quantum curves. It can be rephrased as an eigenvalue equation with eigenvectors corresponding co-dimension 2 defect operators and eigenvalues 4 Wilson surfaces wrapping curve, respectively. Moreover, is generalised v...

A quantisation of chiral symmetry within the Skyrme crystal is carried out. The definition of global isospin in the crystal is explored, and found to be ambiguous. However, the state corresponding to a neutron crystal is identified, and the leading quantum correction to the classical mass is computed. The results are compared to those of Klebanov for a crystal of whole skyrmions.