Applications of Gauge/Gravity Duality to QCD and Heavy Ion Collisions

The description of quarks and gluons, using the theory of quantum chromodynamics (QCD), has been known for a long time. Nevertheless, many fundamental questions in QCD remain unanswered. This is mainly due to problems in solving the theory at low energies, where the theory is strongly interacting. AdS/CFT is a duality between a specific string theory and a conformal field theory. Duality provides new tools to solve the conformal field theory in the strong coupling regime. There is also some evidence that using the duality, one can get at least qualitative understanding of how QCD behaves at strong coupling. In this thesis, we try to address some issues related to QCD and heavy ion collisions, applying the duality in various ways.

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Aspects of Inflationary Models at Low Energy Scales

Cosmological inflation is the dominant paradigm in explaining the origin of structure in the universe. According to the inflationary scenario, there has been a period of nearly exponential expansion in the very early universe, long before the nucleosynthesis. Inflation is commonly considered as a consequence of some scalar field or fields whose energy density starts to dominate the universe. The inflationary expansion converts the quantum fluctuations of the fields into classical perturbations on superhorizon scales and these primordial perturbations are the seeds of the structure in the universe. Moreover, inflation also naturally explains the high degree of homogeneity and spatial flatness of the early universe. The real challenge of the inflationary cosmology lies in trying to establish a connection between the fields driving inflation and theories of particle physics. In this thesis we concentrate on inflationary models at scales well below the Planck scale. The low scale allows us to seek for candidates for the inflationary matter within extensions of the Standard Model but typically also implies fine-tuning problems. We discuss a low scale model where inflation is driven by a flat direction of the Minimally Supersymmetric Standard Model. The relation between the potential along the flat direction and the underlying supergravity model is studied. The low inflationary scale requires an extremely flat potential but we find that in this particular model the associated fine-tuning problems can be solved in a rather natural fashion in a class of supergravity models. For this class of models, the flatness is a consequence of the structure of the supergravity model and is insensitive to the vacuum expectation values of the fields that break supersymmetry. Another low scale model considered in the thesis is the curvaton scenario where the primordial perturbations originate from quantum fluctuations of a curvaton field, which is different from the fields driving inflation. The curvaton gives a negligible contribution to the total energy density during inflation but its perturbations become significant in the post-inflationary epoch. The separation between the fields driving inflation and the fields giving rise to primordial perturbations opens up new possibilities to lower the inflationary scale without introducing fine-tuning problems. The curvaton model typically gives rise to relatively large level of non-gaussian features in the statistics of primordial perturbations. We find that the level of non-gaussian effects is heavily dependent on the form of the curvaton potential. Future observations that provide more accurate information of the non-gaussian statistics can therefore place constraining bounds on the curvaton interactions.

Measuring the Cosmic Microwave Background : Topics along the analysis pipeline

The first quarter of the 20th century witnessed a rebirth of cosmology, study of our Universe, as a field of scientific research with testable theoretical predictions. The amount of available cosmological data grew slowly from a few galaxy redshift measurements, rotation curves and local light element abundances into the first detection of the cos- mic microwave background (CMB) in 1965. By the turn of the century the amount of data exploded incorporating fields of new, exciting cosmological observables such as lensing, Lyman alpha forests, type Ia supernovae, baryon acoustic oscillations and Sunyaev-Zeldovich regions to name a few. -- CMB, the ubiquitous afterglow of the Big Bang, carries with it a wealth of cosmological information. Unfortunately, that information, delicate intensity variations, turned out hard to extract from the overall temperature. Since the first detection, it took nearly 30 years before first evidence of fluctuations on the microwave background were presented. At present, high precision cosmology is solidly based on precise measurements of the CMB anisotropy making it possible to pinpoint cosmological parameters to one-in-a-hundred level precision. The progress has made it possible to build and test models of the Universe that differ in the way the cosmos evolved some fraction of the first second since the Big Bang. -- This thesis is concerned with the high precision CMB observations. It presents three selected topics along a CMB experiment analysis pipeline. Map-making and residual noise estimation are studied using an approach called destriping. The studied approximate methods are invaluable for the large datasets of any modern CMB experiment and will undoubtedly become even more so when the next generation of experiments reach the operational stage. -- We begin with a brief overview of cosmological observations and describe the general relativistic perturbation theory. Next we discuss the map-making problem of a CMB experiment and the characterization of residual noise present in the maps. In the end, the use of modern cosmological data is presented in the study of an extended cosmological model, the correlated isocurvature fluctuations. Current available data is shown to indicate that future experiments are certainly needed to provide more information on these extra degrees of freedom. Any solid evidence of the isocurvature modes would have a considerable impact due to their power in model selection.

Rolling tachyons, random matrices, and Coulomb gas thermodynamics

Time-dependent backgrounds in string theory provide a natural testing ground for physics concerning dynamical phenomena which cannot be reliably addressed in usual quantum field theories and cosmology. A good, tractable example to study is the rolling tachyon background, which describes the decay of an unstable brane in bosonic and supersymmetric Type II string theories. In this thesis I use boundary conformal field theory along with random matrix theory and Coulomb gas thermodynamics techniques to study open and closed string scattering amplitudes off the decaying brane. The calculation of the simplest example, the tree-level amplitude of n open strings, would give us the emission rate of the open strings. However, even this has been unknown. I will organize the open string scattering computations in a more coherent manner and will argue how to make further progress.

Identification of Hadronically Decaying Tau Leptons in Searches for Heavy MSSM Higgs Bosons with the CMS Detector at the CERN LHC

This thesis describes methods for the reliable identification of hadronically decaying tau leptons in the search for heavy Higgs bosons of the minimal supersymmetric standard model of particle physics (MSSM). The identification of the hadronic tau lepton decays, i.e. tau-jets, is applied to the gg->bbH, H->tautau and gg->tbH+, H+->taunu processes to be searched for in the CMS experiment at the CERN Large Hadron Collider. Of all the event selections applied in these final states, the tau-jet identification is the single most important event selection criterion to separate the tiny Higgs boson signal from a large number of background events. The tau-jet identification is studied with methods based on a signature of a low charged track multiplicity, the containment of the decay products within a narrow cone, an isolated electromagnetic energy deposition, a non-zero tau lepton flight path, the absence of electrons, muons, and neutral hadrons in the decay signature, and a relatively small tau lepton mass compared to the mass of most hadrons. Furthermore, in the H+->taunu channel, helicity correlations are exploited to separate the signal tau jets from those originating from the W->taunu decays. Since many of these identification methods rely on the reconstruction of charged particle tracks, the systematic uncertainties resulting from the mechanical tolerances of the tracking sensor positions are estimated with care. The tau-jet identification and other standard selection methods are applied to the search for the heavy neutral and charged Higgs bosons in the H->tautau and H+->taunu decay channels. For the H+->taunu channel, the tau-jet identification is redone and optimized with a recent and more detailed event simulation than previously in the CMS experiment. Both decay channels are found to be very promising for the discovery of the heavy MSSM Higgs bosons. The Higgs boson(s), whose existence has not yet been experimentally verified, are a part of the standard model and its most popular extensions. They are a manifestation of a mechanism which breaks the electroweak symmetry and generates masses for particles. Since the H->tautau and H+->taunu decay channels are important for the discovery of the Higgs bosons in a large region of the permitted parameter space, the analysis described in this thesis serves as a probe for finding out properties of the microcosm of particles and their interactions in the energy scales beyond the standard model of particle physics.

Formation of structure in dark energy cosmologies

Acceleration of the universe has been established but not explained. During the past few years precise cosmological experiments have confirmed the standard big bang scenario of a flat universe undergoing an inflationary expansion in its earliest stages, where the perturbations are generated that eventually form into galaxies and other structure in matter, most of which is non-baryonic dark matter. Curiously, the universe has presently entered into another period of acceleration. Such a result is inferred from observations of extra-galactic supernovae and is independently supported by the cosmic microwave background radiation and large scale structure data. It seems there is a positive cosmological constant speeding up the universal expansion of space. Then the vacuum energy density the constant describes should be about a dozen times the present energy density in visible matter, but particle physics scales are enormously larger than that. This is the cosmological constant problem, perhaps the greatest mystery of contemporary cosmology. In this thesis we will explore alternative agents of the acceleration. Generically, such are called dark energy. If some symmetry turns off vacuum energy, its value is not a problem but one needs some dark energy. Such could be a scalar field dynamically evolving in its potential, or some other exotic constituent exhibiting negative pressure. Another option is to assume that gravity at cosmological scales is not well described by general relativity. In a modified theory of gravity one might find the expansion rate increasing in a universe filled by just dark matter and baryons. Such possibilities are taken here under investigation. The main goal is to uncover observational consequences of different models of dark energy, the emphasis being on their implications for the formation of large-scale structure of the universe. Possible properties of dark energy are investigated using phenomenological paramaterizations, but several specific models are also considered in detail. Difficulties in unifying dark matter and dark energy into a single concept are pointed out. Considerable attention is on modifications of gravity resulting in second order field equations. It is shown that in a general class of such models the viable ones represent effectively the cosmological constant, while from another class one might find interesting modifications of the standard cosmological scenario yet allowed by observations. The thesis consists of seven research papers preceded by an introductory discussion.

Thermodynamics of electroweak matter

The electroweak theory is the part of the standard model of particle physics that describes the weak and electromagnetic interactions between elementary particles. Since its formulation almost 40 years ago, it has been experimentally verified to a high accuracy and today it has a status as one of the cornerstones of particle physics. Thermodynamics of electroweak physics has been studied ever since the theory was written down and the features the theory exhibits at extreme conditions remain an interesting research topic even today. In this thesis, we consider some aspects of electroweak thermodynamics. Specifically, we compute the pressure of the standard model to high precision and study the structure of the electroweak phase diagram when finite chemical potentials for all the conserved particle numbers in the theory are introduced. In the first part of the thesis, the theory, methods and essential results from the computations are introduced. The original research publications are reprinted at the end.

Simulations of dimensionally reduced effective theories of high temperature QCD

Quantum chromodynamics (QCD) is the theory describing interaction between quarks and gluons. At low temperatures, quarks are confined forming hadrons, e.g. protons and neutrons. However, at extremely high temperatures the hadrons break apart and the matter transforms into plasma of individual quarks and gluons. In this theses the quark gluon plasma (QGP) phase of QCD is studied using lattice techniques in the framework of dimensionally reduced effective theories EQCD and MQCD. Two quantities are in particular interest: the pressure (or grand potential) and the quark number susceptibility. At high temperatures the pressure admits a generalised coupling constant expansion, where some coefficients are non-perturbative. We determine the first such contribution of order g^6 by performing lattice simulations in MQCD. This requires high precision lattice calculations, which we perform with different number of colors N_c to obtain N_c-dependence on the coefficient. The quark number susceptibility is studied by performing lattice simulations in EQCD. We measure both flavor singlet (diagonal) and non-singlet (off-diagonal) quark number susceptibilities. The finite chemical potential results are optained using analytic continuation. The diagonal susceptibility approaches the perturbative result above 20T_c$, but below that temperature we observe significant deviations. The results agree well with 4d lattice data down to temperatures 2T_c.

From the LHC to future colliders

Discoveries at the LHC will soon set the physics agenda for future colliders. This report of a CERN Theory Institute includes the summaries of Working Groups that reviewed the physics goals and prospects of LHC running with 10 to 300 fb(-1) of integrated luminosity, of the proposed sLHC luminosity upgrade, of the ILC, of CLIC, of the LHeC and of a muon collider. The four Working Groups considered possible scenarios for the first 10 fb(-1) of data at the LHC in which (i) a state with properties that are compatible with a Higgs boson is discovered, (ii) no such state is discovered either because the Higgs properties are such that it is difficult to detect or because no Higgs boson exists, (iii) a missing-energy signal beyond the Standard Model is discovered as in some supersymmetric models, and (iv) some other exotic signature of new physics is discovered. In the contexts of these scenarios, the Working Groups reviewed the capabilities of the future colliders to study in more detail whatever new physics may be discovered by the LHC. Their reports provide the particle physics community with some tools for reviewing the scientific priorities for future colliders after the LHC produces its first harvest of new physics from multi-TeV collisions.

Primordial Perturbations from a Self-interacting Curvaton

Inflation is a period of accelerated expansion in the very early universe, which has the appealing aspect that it can create primordial perturbations via quantum fluctuations. These primordial perturbations have been observed in the cosmic microwave background, and these perturbations also function as the seeds of all large-scale structure in the universe. Curvaton models are simple modifications of the standard inflationary paradigm, where inflation is driven by the energy density of the inflaton, but another field, the curvaton, is responsible for producing the primordial perturbations. The curvaton decays after inflation as ended, where the isocurvature perturbations of the curvaton are converted into adiabatic perturbations. Since the curvaton must decay, it must have some interactions. Additionally realistic curvaton models typically have some self-interactions. In this work we consider self-interacting curvaton models, where the self-interaction is a monomial in the potential, suppressed by the Planck scale, and thus the self-interaction is very weak. Nevertheless, since the self-interaction makes the equations of motion non-linear, it can modify the behaviour of the model very drastically. The most intriguing aspect of this behaviour is that the final properties of the perturbations become highly dependent on the initial values. Departures of Gaussian distribution are important observables of the primordial perturbations. Due to the non-linearity of the self-interacting curvaton model and its sensitivity to initial conditions, it can produce significant non-Gaussianity of the primordial perturbations. In this work we investigate the non-Gaussianity produced by the self-interacting curvaton, and demonstrate that the non-Gaussianity parameters do not obey the analytically derived approximate relations often cited in the literature. Furthermore we also consider a self-interacting curvaton with a mass in the TeV-scale. Motivated by realistic particle physics models such as the Minimally Supersymmetric Standard Model, we demonstrate that a curvaton model within the mass range can be responsible for the observed perturbations if it can decay late enough.

Search for Maximal Flavor Violating Scalars in Same-Charge Lepton Pairs in pp�� Collisions at ���s=1.96������TeV

Models of Maximal Flavor Violation (MxFV) in elementary particle physics may contain at least one new scalar SU$(2)$ doublet field $\Phi_{FV} = (\eta^0,\eta^+)$ that couples the first and third generation quarks ($q_1,q_3$) via a Lagrangian term $\mathcal{L}_{FV} = \xi_{13} \Phi_{FV} q_1 q_3$. These models have a distinctive signature of same-charge top-quark pairs and evade flavor-changing limits from meson mixing measurements. Data corresponding to 2 fb$^{-1}$ collected by the CDF II detector in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV are analyzed for evidence of the MxFV signature. For a neutral scalar $\eta^0$ with $m_{\eta^0} = 200$ GeV/$c^2$ and coupling $\xi_{13}=1$, $\sim$ 11 signal events are expected over a background of $2.1 \pm 1.8$ events. Three events are observed in the data, consistent with background expectations, and limits are set on the coupling $\xi_{13}$ for $m_{\eta^0} = 180-300$ GeV/$c^2$.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative ���eld theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to ���ll this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm e���ect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satis���ed in the case of a perturbative source for the point-like magnetic monopole.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Sneutrino-antisneutrino oscillations at colliders

Modern elementary particle physics is based on quantum field theories. Currently, our understanding is that, on the one hand, the smallest structures of matter and, on the other hand, the composition of the universe are based on quantum field theories which present the observable phenomena by describing particles as vibrations of the fields. The Standard Model of particle physics is a quantum field theory describing the electromagnetic, weak, and strong interactions in terms of a gauge field theory. However, it is believed that the Standard Model describes physics properly only up to a certain energy scale. This scale cannot be much larger than the so-called electroweak scale, i.e., the masses of the gauge fields W^+- and Z^0. Beyond this scale, the Standard Model has to be modified. In this dissertation, supersymmetric theories are used to tackle the problems of the Standard Model. For example, the quadratic divergences, which plague the Higgs boson mass in the Standard model, cancel in supersymmetric theories. Experimental facts concerning the neutrino sector indicate that the lepton number is violated in Nature. On the other hand, the lepton number violating Majorana neutrino masses can induce sneutrino-antisneutrino oscillations in any supersymmetric model. In this dissertation, I present some viable signals for detecting the sneutrino-antisneutrino oscillation at colliders. At the e-gamma collider (at the International Linear Collider), the numbers of the electron-sneutrino-antisneutrino oscillation signal events are quite high, and the backgrounds are quite small. A similar study for the LHC shows that, even though there are several backrounds, the sneutrino-antisneutrino oscillations can be detected. A useful asymmetry observable is introduced and studied. Usually, the oscillation probability formula where the sneutrinos are produced at rest is used. However, here, we study a general oscillation probability. The Lorentz factor and the distance at which the measurement is made inside the detector can have effects, especially when the sneutrino decay width is very small. These effects are demonstrated for a certain scenario at the LHC.