<p>String theory has proved to be a valuable theoretical laboratory for probing gravity and gauge theory in a unified framework. In this thesis some of the exciting spin-offs of string theory such as branes and higher spin are studied. After a review of the basics of string theory the four papers of the thesis are discussed. In the first paper we support the equivalence between two descriptions of non-commutative open strings by calculating scattering amplitudes in both approaches. The second paper gives a physical interpretation of the fact that Ramond-Ramond charge in string theory on SU(2) is only defined modulo an integer. In the third paper we calculate contributions to the stress-energy tensor of higher-spin theory in four dimensional AdS space, and in the last paper of the thesis we compare the free energy of the two dimesional type 0A extremal blackhole and find agreement with the corresponding quantity in a deformed matrix model.</p>

For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level. A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only. We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.

String theory has proved to be a valuable theoretical laboratory for probing gravity and gauge theory in a unified framework. In this thesis some of the exciting spin-offs of string theory such as branes and higher spin are studied. After a review of the basics of string theory the four papers of the thesis are discussed. In the first paper we support the equivalence between two descriptions of non-commutative open strings by calculating scattering amplitudes in both approaches. The second paper gives a physical interpretation of the fact that Ramond-Ramond charge in string theory on SU(2) is only defined modulo an integer. In the third paper we calculate contributions to the stress-energy tensor of higher-spin theory in four dimensional AdS space, and in the last paper of the thesis we compare the free energy of the two dimesional type 0A extremal blackhole and find agreement with the corresponding quantity in a deformed matrix model.

<p>In this work, we consider the addition of a single neutral massive vector boson to the Standard Model (SM). This boson, which we refer to as N⁰, induces dipolar transitions between electrons and muons. We obtain bounds on the strength of its coupling and its mass: from the scattering process e+e- to mu+mu-; from its contribution to muonium-antimuonium oscillations; and from its possible contribution to the rare muon decay mu- to e+e-e-. In particular, we examine the two cases where the mediator is both heavy and light compared with the scattering energies for, and place constraints on the relevant parameters based on their contributions to the cross section and the forward-backward asymmetry. For muonium-antimuonium oscillations, we consider only the case where the mediator is heavy compared to all other scales, reducing its effect to an effective contact interaction. Finally, we consider an SU(2) invariant theory from which the N⁰ interaction emerges, and find that flavour diagonal interactions also emerge, giving a tree-level path for the decay mu- to e+e-e-. We find that the heavy N⁰ is not strongly constrained by this contribution, while the light N⁰ is very strongly constrained by it. Very generally, we find that the heavy N⁰ is much less constrained than other lepton flavour violating processes, while the constraints on the light N0 vary in strength between processes.</p> / Master of Science (MSc)

<p>This thesis addresses two separate naturalness issues which generically come to bear on physical theories with large extra dimensions, and so a gravity scale much lower than the Planck scale. The first is related to the observed stability of the proton, wherein we determine the relevant constraints on an additional gauge boson which conserves baryon number. Although several such proposals have been previously considered, our analysis is distinctive in its interest in lighter gauge boson masses (which naturally arise in such models), and in its focus on the dependence of constraints due to kinetic mixing effects. The second is related to the main purpose of large extra dimensions---namely, to address the smallness of the observed vacuum energy---wherein we compute the leading-order quantum corrections to the four-dimensional (4D) vacuum energy resulting from loops of extra-dimensional fields. We compute the contributions from bulk scalars (spin 0), fermions (spin 1/2), and gauge fields (spin 1) in a flux-stabilized, spheroidal extra-dimensional geometry whose rugby-ball shape is due to two codimension-2 branes---one at each pole. (We also obtain the corresponding beta functions for both bulk and brane operators.) These results are then combined to obtain the net contribution from various multiplets in the context of a particular supersymmetric extra-dimensional model that has been shown to give a vanishing result for the 4D vacuum energy at the classical level. Surprisingly, we find that supersymmetry can be preserved dynamically at one loop in the case of identical branes, without arranging any particular relationship between the brane parameters. Perturbing away from the case of identical branes is shown to give a positive 1-loop contribution to the 4D vacuum energy whose size is set by the radius of the extra dimensions.</p> / Doctor of Philosophy (PhD)

This thesis concerns a range of aspects of theoretical physics. It is composed of two parts. In the first part we motivate our line of research, and introduce and discuss the relevant concepts. In the second part, four research papers are collected. The first paper deals with a possible extension of general relativity, namely the recently discovered classically consistent bimetric theory. In this paper we study the behavior of perturbations of the metric(s) around cosmologically viable background solutions. In the second paper, we explore possibilities for particle physics with low-scale supersymmetry. In particular we consider the addition of supersymmetric higher-dimensional operators to the minimal supersymmetric standard model, and study collider phenomenology in this class of models. The third paper deals with a possible extension of the notion of Lie algebras within category theory. Considering Lie algebras as objects in additive symmetric ribbon categories we define the proper Killing form morphism and explore its role towards a structure theory of Lie algebras in this setting. Finally, the last paper is concerned with the computation of string amplitudes in four dimensional models with reduced supersymmetry. In particular, we develop general techniques to compute amplitudes involving gauge bosons and gravitons and explicitly compute the corresponding three- and four-point functions. On the one hand, these results can be used to extract important pieces of the effective actions that string theory dictates, on the other they can be used as a tool to compute the corresponding field theory amplitudes. / Over the last twenty years there have been spectacular observations and experimental achievements in fundamental physics. Nevertheless all the physical phenomena observed so far can still be explained in terms of two old models, namely the Standard Model of particle physics and the ΛCDM cosmological model. These models are based on profoundly different theories, quantum field theory and the general theory of relativity. There are many reasons to believe that the SM and the ΛCDM are effective models, that is they are valid at the energy scales probed so far but need to be extended and generalized to account of phenomena at higher energies. There are several proposals to extend these models and one promising theory that unifies all the fundamental interactions of nature: string theory. With the research documented in this thesis we contribute with four tiny drops to the filling of the fundamental physics research pot. When the pot will be saturated, the next fundamental discovery will take place.

This thesis contributes with a number of topics to the subject of string compactifications, especially in the instance of the E₈ × E₈ heterotic string theory compactified on smooth Calabi-Yau threefolds. In the first half of the work, I discuss the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties. The intricate structure of this plot is explained by the existence of certain webs of elliptic-K3 fibrations, whose mirror images are also elliptic-K3 fibrations. Such manifolds arise from reflexive polytopes that can be cut into two parts along slices corresponding to the K3 fiber. Any two half-polytopes over a given slice can be combined into a reflexive polytope. This fact, together with a remarkable relation on the additivity of Hodge numbers, give to the Hodge plot the appearance of a fractal. Moving on, I discuss a different type of web of manifolds, by looking at smooth Z₃-quotients of Calabi-Yau three-folds realised as complete intersections in products of projective spaces. Non-simply connected Calabi-Yau three-folds provide an essential ingredient in heterotic string compactifications. Such manifolds are rare in the classical constructions, but they can be obtained as quotients of homotopically trivial Calabi-Yau three-folds by free actions of finite groups. Many of these quotients are connected by conifold transitions. In the second half of the work, I explore an algorithmic approach to constructing E₈ × E₈ heterotic compactifications using holomorphic and poly-stable sums of line bundles over complete intersection Calabi-Yau three-folds that admit freely acting discrete symmetries. Such Abelian bundles lead to N = 1 supersymmetric GUT theories with gauge group SU(5) × U(4) and matter fields in the 10, ⁻10, ⁻5, 5 and 1 representations of SU(5). The extra U(1) symmetries are generically Green-Schwarz anomalous and, as such, they survive in the low energy theory only as global symmetries. These, in turn, constrain the low energy theory and in many cases forbid the existence of undesired operators, such as dimension four or five proton decay operators. The line bundle construction allows for a systematic computer search resulting in a plethora of models with the exact matter spectrum of the Minimally Supersymmetric Standard Model, one or more pairs of Higgs doublets and no exotic fields charged under the Standard Model group. In the last part of the thesis I focus on the case study of a Calabi-Yau hypersurface embedded in a product of four CP1 spaces, referred to as the tetraquadric manifold. I address the question of the finiteness of the class of consistent and physically viable line bundle models constructed on this manifold. Line bundle sums are part of a moduli space of non-Abelian bundles and they provide an accessible window into this moduli space. I explore the moduli space of heterotic compactifications on the tetraquadric hypersurface around a locus where the vector bundle splits as a direct sum of line bundles, using the monad construction. The monad construction provides a description of poly-stable S(U(4) × U(1))–bundles leading to GUT models with the correct field content in order to induce standard-like models. These deformations represent a class of consistent non-Abelian models that has co-dimension one in Kähler moduli space.

This thesis reviews the method of Mafra, Schlotterer, and Stieberger (2011) for computing the full colour ordered N-point open superstring amplitude using the Pure Spinor formalism. We introduce relevant elements of super Yang-Mills theory and examine the basics of the Pure Spinor formalism, with a focus on tools for amplitude computation. We then define a series of objects with increasingly useful BRST transformation properties, which greatly simplify the calculations, and show how these properties can be determined using a diagrammatic method. Finally, we use the explicit four- and five-point amplitude computations as stepping stones to compute the general N-point amplitude, which factors into a set of kinematic integrals multiplying SYM subamplitudes.

One of the phenomenal results emerging from string theory is the AdS/CFT correspondence or gauge-gravity duality: In certain cases a theory of gravity is equivalent to a "dual" gauge theory, very similar to the one describing non-gravitational interactions of fundamental subatomic particles. A difficult problem on one side can be mapped to a simpler and solvable problem on the other side using this correspondence. Thus one of the theories can be understood better using the other. The mapping between theories of gravity and gauge theories has led to new approaches to building models of particle physics from string theory. One of the important features to model is the phenomenon of confinement present in strong interaction of particle physics. This feature is not present in the gauge theory arising in the simplest of the examples of the duality. However this N = 4 supersymmetric Yang-Mills gauge theory enjoys the property of being integrable, i.e. it can be exactly solved in terms of conserved charges. It is expected that if a more realistic theory turns out to be integrable, solvability of the theory would lead to simple analytical expressions for quantities like masses of the hadrons in the theory. In this thesis we show that the existing models of confinement are all nonintegrable--such simple analytic expressions cannot be obtained. We moreover show that these nonintegrable systems also exhibit features of chaotic dynamical systems, namely, sensitivity to initial conditions and a typical route of transition to chaos. We proceed to study the quantum mechanics of these systems and check whether their properties match those of chaotic quantum systems. Interestingly, the distribution of the spacing of meson excitations measured in the laboratory have been found to match with level-spacing distribution of typical quantum chaotic systems. We find agreement of this distribution with models of confining strong interactions, conforming these as viable models of particle physics arising from string theory.

In the first part of this thesis we study baryonic U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Such short multiplets originate from the Kaluza-Klein compactification of eleven-dimensional supergravity on the corresponding Sasaki-Einstein seven-manifolds. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, which we classify, and propose for them field theory duals. We then study in detail the cone over the well-known Sasaki-Einstein space Q^111, which is a U(1) fibration over CP^1 x CP^1 x CP^1. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and M5 branes wrapping five-cycles in the Q^111 space. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We then study the implications of turning on a closed three-form with non-zero periods through torsion three cycles in the Sasaki-Einstein manifold. This three-form, otherwise known as torsion G-flux, non-trivially affects the supergravity dual of Higgsing, and we show that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^1,2(CP^2), which is a S^3 bundle over CP^2. We then explain how the choice of M-theory circle in the background can result in exotic renormalization group flows in the dual field theory, and study this in detail for the Sasaki-Einstein manifold Y^1,2(CP^2). We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Sasaki-Einstein Q^222 example, which is a Z_2 orbifold of Q^111 in which the free Z_2 quotient is along the R-symmetry U(1) fibre. The holographic interpretation of such instantons is currently unclear. In the second part of this thesis we study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at Calabi-Yau three-fold singularities. This leads, for particular vacuum expectation values, to the emergence of non-anomalous baryonic symmetries during the renormalization group flow. We identify these vacuum expectation values with critical values of the NS-NS B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold theory and the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries, and identify the expected Goldstone bosons and global strings in the infra-red. In doing so we confirm the claim that the emerging symmetries are indeed non-anomalous baryonic symmetries.