The Noether charge algebra of brane actions is typically modified by a topological anomalous term. The underlying cohomology of this anomalous term is investigated, and it is shown that the anomalous term possesses a gauge freedom. The result is that the anomalous term generates a parameterized family of topological charge algebras. When fermionic charges are taken to be nonvanishing, the known algebras underlying extended superspace formulations of the action appear in these families. This phenomena is investigated for minimal p-branes, Dp-branes and (p, q)-strings. The algebras resulting from the D-brane actions are shown to allow the construction of extended superspace actions without worldvolume gauge fields. It is shown that the actions are !-symmetric, and that the symmetry is generated by a right action. The global and local symmetry transformations of the Born-Infeld gauge field are thus shown to be described geometrically by left/right actions of the underlying extended supertranslation group. An equivalence class construction is proposed for the description of compact fermionic dimensions. In this construction, open strings in extended superspace translate to closed strings in compact superspace, and fermionic topological charges may be realized by closed strings. The differential underlying the descent construction for Noether charge algebras is shown to be naturally described as a dual of the de Rham differential. The ghost fields used in the construction are shown to be described geometrically as a vielbein with respect to this differential.

We replaced the classical string theory notions of parameter space and world-time with noncommutative tori and consider maps between these spaces. The dynamics of mappings between different noncommutative tori were studied and a noncommutative generalization of the Polyakov action was derived. The quantum torus was studied in detail as well as *-homomorphisms between different quantum tori. A finite dimensional representation of the quantum torus was studied and the partition function and other path integrals were calculated. At the end we proved existence theorems for mappings between different noncommutative tori. / Dissertation (MSc)--University of Pretoria, 2012. / Physics / unrestricted

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The experiments performed at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab have discovered a state of matter called the strongly coupled quark-gluon plasma (sQGP). The strong coupling has limited the ability of the standard theory to describe such matter, namely Quantum Chromodynamics (QCD). However, string theory's anti-de Sitter/conformal field theory (AdS/CFT) correspondence has provided a new way to study the situation and in an analytical manner. So far, hydrodynamic properties of RHIC's plasma, such as elliptic flow and longitudinal expansion, have been seen to follow from classical supergravity calculations. In this dissertation I discuss some of the field's development as well as the research done by the author and collaborators.

This thesis deals with phenomenological and theoretical aspects of cosmoparticle physics and string theory. There are many open questions in these topics. In connection with cosmology we would like to understand the detailed properties of dark matter, dark energy, generation of primordial perturbations, etc., and in connection with particle physics we would like to understand the detailed properties of models that stabilize the electroweak scale, for instance supersymmetry. At the same time, we also need to understand these issues in a coherent theoretical framework. Such a framework is offered by string theory. In this thesis, I analyze the interplay between Higgs and dark matter physics in an effective field theory extension of the minimally supersymmetric standard model. I study a theory of modified gravity, where the graviton has acquired a mass, and show the explicit implementation of the Vainshtein mechanism, which allows one to put severe constraints on the graviton mass. I address the question of Planck scale corrections to inflation in string theory, and show how such corrections can be tamed. I study perturbations of warped throat regions of IIB string theory compactifications and classify allowed boundary conditions. Using this analysis, I determine the potential felt by an anti-D3-brane in such compactifications, using the explicit harmonic data on the conifold. I also address questions of perturbative quantum corrections in string theory and calculate one-loop corrections to the moduli space metric of Calabi-Yau orientifolds. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows:<strong>  </strong>Paper 3: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript.</p>

This thesis is devoted to the study of two important applications of gauge-gravity duality: the cosmological singularity problem and conformal fluid dynamics. Gauge-gravity duality is a concrete dual relationship between a gauge theory (such as electromagnetism, the theories of weak and strong interactions), and a theory of strings which contains gravity. The most concrete application of this duality is the AdS/CFT correspondence, where the theory containing gravity lives in the bulk of an asymptotically anti-de-Sitter space-time, while the dual gauge theory is a deformation of a conformal field theory which lives on the boundary of anti-de-Sitter space-time(AdS). Our first application of gauge-gravity duality is to the cosmological singularity problem in string gravity. A cosmological singularity is defined as a spacelike region of space-time which is highly curved so that Einstein’s gravity theory can be no longer applied. In our setup the bulk space-time has low curvature in the far past and the physics is well described by supergravity (which is an extension of standard Einstein gravity). The cosmological singularity is driven by a time dependent string coupling in the bulk theory. The rate of change of the coupling is slow, but the net change of the coupling can be large. The dual description of this is a time dependent coupling of the boundary gauge theory. The coupling has a profile which is a constant in the far past and future and attains a small but finite value at intermediate times. We construct the supergravity solution, with the initial condition that the bulk space-time is pure AdS in the far past and show that the solution remains smooth in a derivative expansion without formation of black holes. However when the intermediate value of the string coupling becomes weak enough, space-time becomes highly curved and the supergravity approximation breaks down, mimicking a spacelike singularity. The resulting dynamics is analyzed in the dual gauge theory with a time dependent coupling constant which varies slowly. We develop an appropriate adiabatic expansion in the gauge theory in terms of coherent states and show that the time evolution continues to be smooth. We cannot, however, arrive at a definitive conclusion about the fate of the system at very late times when the coupling has again risen and supergravity again applies. One possibility is that the energy which has been supplied to the universe is simply extracted out and the space-time goes back to its initial state. This could provide a model for a bouncing cosmology. A second possibility is that dissipation leads to a thermal state at late time. If this possibility holds, we show that such a thermal state will be described either by a gas of strings or by a small black hole, but not by a big black hole. This means that in either case, the future space-time is close to AdS. We then apply gauge-gravity duality to conformal fluid dynamics. The long wavelength behavior of any strongly coupled system with a finite mean free path is described by an appropriate fluid dynamics. The bulk dual of a fluid flow in the boundary theory is a black hole with a slowly varying horizon. In this work we consider certain fluid flows which become supersonic in some regions. It is well known that such flows present acoustic analogs of ergoregions and horizons, where acoustic waves cannot propagate in certain directions. Such acoustic horizons are expected to exhibit thermal radiation of acoustic waves with temperature essentially given by the gradient of the velocity at the acoustic horizon. We find acoustic analogs of black holes in charged conformal fluids and use gauge-gravity duality to construct dual gravity solutions. A certain class of gravitational quasinormal wave modes around these gravitational backgrounds perceives a horizon. Upon quantization, this implies that these gravitational modes should have a thermal spectrum. The final issue that we study is fluid-gravity duality at zero temperature. The usual way of constructing gravity duals of fluid flows is by means of a small derivative expansion, in which the derivatives are much smaller than the temperature of the background black hole. Recently, it has been reported that for charged fluids, this procedure breaks down in the zero temperature limit. More precisely, corrections to the small derivative expansion in the dual gravity of charged fluid at zero temperature have singularities at the black hole horizon. In this case, fluid-gravity duality is not understood precisely. We explore this problem for a zero temperature charged fluid driven by a low frequency, small amplitude and spatially homogeneous external force. In the gravity dual, this force corresponds to a time dependent boundary value of the dilaton field. We calculate the bulk solution for the dilaton and the leading backreaction using a modified low frequency expansion. The resulting solutions are regular everywhere, establishing fluid-gravity duality to this order.

<p>Defended on November 3rd, 2011</p> / <p>In this thesis, we describe the properties of brane worlds embedded in a spacetime with two extra dimensions. We derive and describe the boundary conditions that branes impose on the bulk fields in the theory, and show that they reproduce known results for D7 branes in F-theory compactifications of type IIB supergravity. We show how brane-bulk couplings can stabilize moduli of a flux stabilized compactification of extra dimensions. An important new ingredient is that the branes can have a magnetic coupling to the flux that stabilizes the bulk. This coupling allows the system to relax the stringent constraints of flux quantization, which allows the bulk spacetime to respond to perturbations of the branes. We derive the dynamics of the lower-dimensional effective theory below the Kaluza-Klein scale, and show that the contributions of the magnetic coupling can be competitive with the tension of the brane. We first describe the simplest flux compactification: an Einstein-scalar- Maxwell theory in 6 dimensions. We find that the effective potential in 4 dimensions gets minimized at the position one would naively expect - at the stationary point of the sum of all the brane Lagrangians - but its value at the minimum gets changed by the magnetic coupling to the brane. Next we find that if the bulk is described by 6 dimensional gauged chiral supergravity, the effect of the magnetic coupling allows the curvature on the brane to be suppressed relative to the generic scale of the tension on the branes. We use this observation to construct an explicit brane-bulk system that has a technically natural cosmological constant of the correct size. The classical on-brane curvature vanishes in our construction, and the first order quantum corrections give a value to the cosmological constant of the right order of magnitude. We estimate higher loop corrections, and they are greatly suppressed.</p> / Doctor of Philosophy (PhD)

This thesis is concerned with Calabi-Yau threefolds and vector bundles upon them, which are the basic mathematical objects at the centre of smooth supersymmetric compactifications of heterotic string theory. We begin by explaining how these objects arise in physics, and give a brief review of the techniques of algebraic geometry which are used to construct and study them. We then turn to studying multiply-connected Calabi-Yau threefolds, which are of particular importance for realistic string compactifications. We construct a large number of new examples via free group actions on complete intersection Calabi-Yau manifolds (CICY's). For special values of the parameters, these group actions develop fixed points, and we show that, on the quotient spaces, this leads to a particular class of singularities, which are quotients of the conifold. We demonstrate that, in many cases at least, such a singularity can be resolved to yield another smooth Calabi-Yau threefold, with different Hodge numbers and fundamental group. This is a new example of the interconnectedness of the moduli spaces of distinct Calabi-Yau threefolds. In the second part of the thesis we turn to a study of two new `three-generation' manifolds, constructed as quotients of a particular CICY, which can also be represented as a hypersurface in dP6 x dP6, where dP6 is the del Pezzo surface of degree six. After describing the geometry of this manifold, and especially its non-Abelian quotient, in detail, we show how to construct on the quotient manifolds vector bundles which lead to four-dimensional heterotic models with the standard model gauge group and three generations of particles. The example described in detail has the spectrum of the minimal supersymmetric standard model plus a single vector-like pair of colour triplets.