In this thesis we study several aspects of gauge/gravity dualities. We start by analyzing the structure of the UV divergences of the Wilson loop for a general gauge/gravity duality. We find that, due to the presence of a nontrivial NSNS B-field and metric, new divergences that cannot be subtracted out by the conventional Legendre transform may arise. We also derive conditions on the B-field and the metric, which when satisfied, the leading UV divergence will become linear, and can be canceled out by choosing the boundary condition of the string appropriately. Our results, together with the result of [15], where the effect of a nontrivial dilaton on the structure of UV divergences in Wilson loop is analyzed, allow us to conclude that Legendre transform is at best capable of canceling the linear UV divergences arising from the area of the worldsheet, but is incapable to handle the divergences associated with the dilaton or the B-field in general. We also solve the conditions for the cancelation of the leading linear divergences generally and find that many well-known super gravity backgrounds are of these kinds, including examples such as the Sakai-Sugimoto QCD model or N = 1 duality with Sasaki-Einstein spaces. We also point out that Wilson loop in the Klebanov-Strassler background have a divergence associated with the B-field which cannot be canceled away with the Legendre transform. Moreover, our results indicate that the finiteness of the expectation value of the Wilson loop does not depend on the supersymmetry. In the next chapter, we propose a definition of the Wilson loop operator in the N = 1 ß-deformed supersymmetric Yang-Mills theory. Although the operator is not BPS, it has a finite expectation value, result that come from the work in the previous chapter but also from the field theory calculations at least up to order (9(^2)N)(^2). We also derive the general form of the boundary condition satisfied by the dual string worldsheet and find that it is deformed. Finiteness of the expectation value of the Wilson loop, together with some rather remarkable properties of the Lunin-Maldacena metric and the B-field, fixes the boundary condition to be one which is characterized by the vielbein of the deformed supergravity metric. The Wilson loop operators provide natural candidates as dual descriptions to some of the existing D-brane configurations in the Lunin-Maldacena background. We also construct the string dual configuration for a near-1/4 BPS circular Wilson loop operator. The string lies on a deformed three-sphere instead of a two-sphere as in the undeformed case. The expectation value of the Wilson loop operator is computed using the AdS/CFT correspondence and is found to be independent of the deformation. In the next chapter we focus on a different topic, and find point-like and classical string solutions on the AdS(_5) x X(^5), where are the 5-dimensional Sasaki-Einstein manifolds Y(^p,q) and L(^p.q.r). The number of acceptable solutions is limited drastically in order to satisfy the constraints on the parameters and coordinates of the manifolds. We find the energy-spin relations of the above solutions and see that they depend on the parameters of the Sasaki-Einstein manifolds. A discussion on BPS solutions is presented as well. In the last chapter we present a general discussion on topics which related closely to all previous chapters. Among other things we also give some comments on the form of the Wilson loop operator in the ABJM superconformal Chern-Simons theory.

The time evolution operator of quantum field theory (Schrödinger functional) can be written in terms of particles moving on S(^1)/Z(_2-). By deriving the 'gluing property’ which joins two propagators across fixed time surfaces, we show that the Feynman diagram expansion of the free Schrödinger functional is determined once we know the field propagator. We generalise the gluing property to a new method of sewing string field propagators and construct the string field Schrödinger functional in terms of strings moving on S(^1)/Z(_2-). Timelike T-duality in string theory then appears as a large/small time symmetry of string field theory with an exchange of boundary states and string backgrounds. All of our arguments apply equally to the open and closed string. The addition of interactions to quantum field theory bring no complication to our arguments, but modifications are required when the interaction is non-local. As application of these methods we construct the interacting string field vacuum wave functional using knowledge of the vacuum expectation values it must generate.

The study of systems formed from ultracold atomic gases has emerged to become one of the most active research elds within the condensed matter landscape. These highly controllable macroscopic systems amalgamate ideas from many sub disciplines of physics, including the study of low temperatures, quantum optics and quantum information theory as well as the seemingly disparate eld of high energy physics. The central concept of this thesis is gauge theories as applied to systems of bosonic atoms, which at temperatures close to absolute zero form Bose-Einstein condensates. To simulate the mathematical structure of a gauge theory, the geometric (Berry) phase formalism is adopted. This is in turn accomplished by considering the adiabatic following of the eigenstates of the light-matter coupling for an ensemble of atoms forming a Bose-Einstein condensate. These concepts are then applied to show how one can generate a spin-orbit coupling in a one-dimensional condensate, which additionally features a random mass term that allows us to study the physics of Anderson localization in an intriguing \quasi" relativistic regime. One of the features of light induced gauge potentials is that they are static; in the sense that there is no feedback between the light-matter interaction and the matter eld. In the second part of this thesis it is demonstrated how such a feedback mechanism can be induced by the appropriate modi cation of the light-matter interaction. The consequences this has for the condensate are then described at the mean- eld level, including the expected experimental signatures of the resulting `interacting' gauge theory, in terms of the expansion of the condensate and also the structure of the solitons of this nonlinear system. Finally, this nonlinear model is applied to a double well system, from which the associated Bose-Hubbard model is derived and analysed; and the nonlinear Josephson problem studied.

No description available.

The work contained in Part I of this thesis is clearly divided into three distinct sections, each of which deals with a separate aspect of the subject. In Chapter 1, the elastic electromagnetic scattering of two spin 1/2 particles is discussed in the one—photon—exchange approximation, allowing for the possibility of structure of both fermions by means of form factors. Covariant notation is employed throughout, and the algebraic form of the resulting formulae leads naturaly to the use of certain combinations of the Dirac and Pauli form factors rather than these functions themselves. These new 'electric' and 'magnetic' form factors are discussed in detail, and adapted for use in all subsequent work. The formalism is then applied to a discussion of the scattering of muons by protons, and the annihilation of proton—antiproton pairs into lepton pairs; with particular reference to the possibility of detecting a structure of the muon. In Chapter 2, the second order electromagnetic corrections to the above processes are discussed in the framework of an effective perturbation theoretic treatment of the exchange of resonances in the two—photon channel. The possibility of detecting such effects in the process of electron—proton scattering is then considered in this formalism. Chapter 3 contains a calculation of the isovector nucleon form factors by means of unsubtracted dispersion relations. The method of Singh and Udgaonkar is applied to the new form factors with the pleasing result that reasonable figures are obtained for the static values of both the electric and magnetic form factors simultaneously. Part II of the thesis is an investigation of the possibility of using a second rank tensor field to describe a relativistic local spin-2 field. The difficulties involved are discussed in detail, and, in the absence of a complete solution of the problem, a non-local theory is developed for use in Chapter 2 of part I of this thesis.

The central theme in this thesis is compactifications: reductions of higher dimensional theories to lower dimensions and how the geometry of the compactification manifold determines features of the low energy physics. This is studied in the context of non-perturbative string theory in the framework of M-theory and F-theory. Supersymmetry requires the compactification manifold in F-theory to be an elliptically fibered Calabi-Yau, where the complex structure of the elliptic fibration is identified with the complexified coupling constant in type IIB string theory. The non-perturbative nature of the theory originates from the strong-weak duality of type IIB, which manifests itself as the SL(2;Z) modular transformation of the complex structure. Non-abelian gauge symmetries arise naturally in this framework and engineering Grand Uni ed Theories within F-theory has been an active area of research. Compactifications on Calabi-Yau four-folds give rise to gauge theories with N = 1 supersymmetry in four dimensions coupled to gravity. In the first part of this thesis we focus on abelian gauge symmetries in F-theory, which are essential in SU(5) GUTs for forbidding couplings which result in fast proton decay. These arise from rational sections in the elliptic fibration and from the geometric constraints on these sections one can determine the set of possible U(1) charges of GUT matter representations. Armed with this constrained set of charges we then proceed to study the phenomenology of these abelian gauge symmetries in the context of SU(5) GUT models. We analyse their e ectiveness at suppressing proton decay operators and explore the types of realistic flavour textures that can be generated using the Froggatt-Nielsen mechanism. In the latter part of this thesis the focal point changes to M5-branes, one of the two fundamental objects of M-theory. The theory of multiple M5-branes is known to be a 6d N = (2; 0) superconformal eld theory, of which only the space-time symmetries and abelian equations of motion have been determined. In spite of this, fascinating correspondences have been shown to arise from the reduction of the M5-brane theory to lower dimensions. In particular, supersymmetric observables in the reduced theories capture non-trivial aspects of the geometry of the compactification manifold. The final chapter of this thesis studies the compactification of the 6d N = (2; 0) theory on the two-sphere as a step towards deriving a correspondence related to four-manifolds.

We use dynamical mean field theory to investigate the nature of self assembled super-lattices of strong correlated adatoms on metallic surfaces, motivated by the realisation of a Ce super-lattice on an Ag(111) surface, which invites interest as a significant step in our understanding and manipulation of complex nano-scale systems and in the development of technological applications such as atomic scale memory devices. We build upon previous tight binding studies by using the Anderson impurity model to describe a collection of one band strongly correlated impurities on a surface, which exhibit an on-site Coulomb repulsion U when doubly occupied and can hybridise with the adsorbed surface states. We set out the DMFT framework used, explaining how we employ the Hubbard 1 approximation and exact diagonalisation impurity solvers to self consistently include the strong Hubbard U interaction. We discuss the mathematical methods used in the course of our calculations and the computational techniques which make our simulations more time and memory efficient. Our results explore the effect that changing numerous model parameters such as U, total electron density and adatom separation has on several impurity quantities, including occupation, magnetic moment and effective mass/Z function. We consider spectral functions and band structures to gain insight into changes in system behaviour due to these variations. We find that the system contains many competing interactions which produce a complex array of phenomena. We conclude that our work gives insight into the behaviour of self assembled super-lattices, suggesting the inclusion of U is important for understanding the rarity of such systems. We discuss the myriad ways in which this topic should be further studied and outline the future work to be done in improving this method and applying it to diverse problems such as disorder and cluster effects such as RKKY.

No description available.

The research presented in this thesis focuses on electromagnetic (EM) waves generation in photonic crystals (PC). A 2D PC with defect(s) can act as a standing-wave resonator that allows only selected resonances to be confined in the defect(s). In this thesis, two single-defect metallic PCs working at 9.532 GHz were designed, fabricated and characterised, and assembled together to a two-PC module similar to a two-cavity klystron. The two-PC module velocity-modulated a low current electron beam and exchanged energy with the beam in ultra high vacuum (UHV). The observed output spectrum indicated that a unique state was confined. Measured output power observed when varying the input power, DC beam current and voltage agre~d well with theoretical and numerical estimations. For multi-beam applications, multi-defect PCs with multiple splitted resonant states were theoretically and numerically investigated. A dual-state 6-beam 2-PC klystron based on a 6-defect PC numerically demonstrated good gain at S-band (2 to 4 GHz) with low current beams. A new concept of compact PC based accelerator integrating a 6-beam klystron and an acceleration cell was introduced through discussions of 7-defect PCs. Limitations and possible improvement of such a structure were analysed and discussed.

One of the most striking examples of duality correspondence between gauge theories and string theories is the AdS/CFT duality. It relates the type IIB superstring theory on AdS5 x 5 5 to 4-dimensional N = 4 Yangs Mills in its superconformal phase. However, the quantisation of string theory on curved backgrounds appears to be notoriously difficult rendering direct tests of the conjecture elusive. One way to circumvent this problem is by taking the Penrose limit of the AdS5 x 5 5 geometry to obtain the pp-wave background where string theory is soluble. The corresponding limit in gauge theory is to restrict to particular class of" long" operators called BMN operators. It is this correspondence we study in the first part of this thesis. In particular, we provide with a number of rigorous tests of the BMN correspondence beyond the supergravity limit, that probe the truly quantum realm of string theory. By exploring the correspondence, we learn how the correspondence is realised and how the 3-string amplitudes can be obtained purely from perturbative gauge theory calculations for almost all species of string excitations. We also clarify the role of the Z2 symmetry the pp-wave background possesses and discuss the consequences this symmetry has on the choice of the 3-string vertex. There is another type of duality which relates the same N = 4 SYM to a different string theory. This is a weak-to-weak coupling duality recently proposed by Witten. It states that tree level amplitudes of N = 4 SYM can be reproduced by integrating over the moduli space of certain D-instantons in open topological B-model in super-twistor space. This duality has inspired a novel diagrammatic method for calculating