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Confinement and the infrared behaviour of the gluon propagatorBüttner, Kirsten January 1996 (has links)
We investigate the infrared behaviour of the gluon propagator in Quantum Chromo- dynamics (QCD). A natural framework for such a non-perturbative study is the complex of Schwinger-Dyson equations (SDE).The possible infrared behaviour of the gluon, found by self-consistently solving the approximate boson SDE, is studied analytically. We find that only an infrared enhanced gluon propagator, as singular as 1/p(^4) as p(^2) → 0, is consistent and demonstrate why softer solutions, that others have found, are not allowed. Reassuringly the consistent, enhanced infrared behaviour is indicative of the confinement of quarks and gluons, implying, for example, area-law behaviour of the Wilson loop operator and forbidding a Kāllen-Lehmann spectral representation of both quark and gluon propagators. We then briefly consider the implications of these results for models of the pomeron. The enhancement of the gluon propagator does however introduce infrared divergences in the SDE and these need to be regularised. So far model forms of the enhanced gluon propagator have been used in studies of dynamical chiral symmetry breaking and hadron phenomenology. Though very encouraging results have been obtained, one might hope to use the gluon propagator obtained directly from non-perturbative QCD to calculate hadron observables. We therefore attempt to eliminate the infrared divergences in the SDEs in a self- consistent way, entirely within the context of the calculational scheme. To do this we introduce an infrared regulator λ in the truncated gluon SDE in quenched QCD. We find that this regulator is indeed determined by the equation and bounded by the QCD-scale Aqcd- Thus it is possible to perform the regularisation within the SDEs. However, we have not been able to choose λ < Aqcd.
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Perturbative quantization of superstring theory in Anti de-Sitter spacesSundin, Per 19 April 2011 (has links)
Um das mikroskopische Verhalten der Gravitation zu beschreiben, ist es nötig, Quantenfeldtheorie und allgemeine Relativitätstheorie in einer vereinheitlichten Sprache zu formulieren. Eine Möglichkeit dieses Problem anzugehen ist es, die Punktteilchen der Quantenfeldtheorie durch fadenförmige Strings zu ersetzen. Allerdings erfordert die mathematische Konsistenz, dass sich die String in höherdimensionalen Raum-Zeiten bewegen; dies macht es jedoch sehr schwer, physikalische Konsequenzen zu extrahieren. Eine mögliche Lösung dieses Problems ist die Verwendung von String-Dualitäten, welche die Stringtheorie mittels holographischer Beschreibungen mit Eichtheorien auf dem Rand der Raum-Zeit verbinden. Die Dualitäten sind begründete Vermutungen, die die String- und Eichtheorie bei unterschiedlichen Werten der Kopplung gleichsetzen. Nicht zuletzt deshalb ist eine direkte Überprüfung der Dualitäten schwierig durchführbar. Hier hilft jedoch die sehr bemerkenswerte Tatsache, dass eine verborgene Eigenschaft der Vermutungen Integrabilität zu sein scheint, welche eine Extrapolation zwischen starker und schwacher Kopplung ermöglicht. Desweiteren kann das gesamte Spektrum, in gewissen vereinfachenden Grenzfällen, durch einen kompakten Satz von Bethe-Gleichungen ausgedrückt werden. Die Bethe-Gleichungen, welche aus Eichtheorierechnungen hergeleitet und geraten werden, bieten ein exzellentes Hilfsmittel, die vermuteten Dualitäten zu prüfen. Durch das Vergleichen der Vorhersagen der Gleichungen und expliziten Berechnungen in der Stringtheorie erhält man starke Argumente für die Gültigkeit der Vermutung und der angenommenen Integrabilität. / In this thesis we study superstring theory on AdS$_5\, \times\,$S$^5$, AdS$_3\,\times\,$S$^3$ and $\adsfour$. A shared feature of each theory is that their corresponding symmetry algebras allows for a decomposition under a $\mathbb{Z}_4$ grading. The grading can be realized through an automorphism which allows for a convenient construction of the string Lagrangians directly in terms of graded components. We adopt a uniform light-cone gauge and expand in a near plane wave limit, or equivalently, an expansion in transverse string coordinates. With a main focus on the two critical string theories, we perform a perturbative quantization up to quartic order in the number of fields. Each string theory is, through holographic descriptions, conjectured to be dual to lower dimensional gauge theories. The conjectures imply that the conformal dimensions of single trace operators in gauge theory should be equal to the energy of string states. What is more, through the use of integrable methods, one can write down a set of Bethe equations whose solutions encode the full spectral problem. One main theme of this thesis is to match the predictions of these equations, written in a language suitable for the light-cone gauge we employ, against explicit string theory calculations. We do this for a large class of string states and the perfect agreement we find lends strong support for the validity of the conjectures.
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