Zayakin, Andrey (2011): Properties of the Vacuum in Models for QCD: Holography vs. Resummed Field Theory. A Comparative Study. Dissertation, LMU München: Faculty of Physics 

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Abstract
This Thesis is dedicated to a comparison of the two means of studying the electromagnetic properties of the QCD vacuum  holography and resummed field theory. In the UV range the nonpertubative QCD effects play an insignificant role and the dynamics of the theory is exactly predicted by the perturbation theory. On the contrary, the IR physics (e.g. light meson spectra and decays) is very sensitive to the nonperturbative features of the theory. Archetypal examples of a nonperturbative parameter in QCD are gluon condensate and quark condensate. Condensates enter into many lowenergy observables and thus are directly experimentrelated. On the other hand, the power of modern experimental laserphysics facilities being planned (e.g. the ELI project) is already almost reaching the boundary of quark scales (though not hadron scales yet). Thus the dynamics of the condensates is of special importance. Yet little is known about the generation mechanism of either of the condensates and various hypotheses are on the market. Therefore, a modelbuilding approach might be useful here. In this Thesis I compare two classes of distinct models for the dynamics of the condensates. The first class consists of the socalled holographic models of QCD. Based upon the Maldacena conjecture, it tries to establish the properties of QCD correlation functions from the behavior of classical solutions of field equations in a higherdimensional theory. The advantage of the holographic models is that they render a stronglycoupled fourdimensional gauge theory as a dual of some weaklycoupled string/supergravity. This is actually the reason of the immense popularity of holographic models nowadays. The problem of these models is their relevance to actual QCD. None of the models currently on the market is supposed to be ``exactly'' dual to reallife QCD. The possible shortcomings of duality are the presence of extra particles in the spectrum, remaining supersymmetries, wrong reproduction of the meson and baryon spectra etc. Yet in many aspects the holographic approach has been found to be in an excellent agreement with data. These successes are the prediction of the very small viscositytoentropy ratio and the predictions of meson spectra up to 5\% accuracy in several models. On the other hand, the resummation methods in field theory have not been discarded so far. There exists a whole industry of resummation for the correlators in QCD, by means of integral equations, DysonSchwinger equations first of all. Nonlocal observables, such as Wilson loops, are also subjects to resummations, as proposed by Erickson and Zarembo. The success of resummation methods was marked by the agreement of lattice calculations of Green functions with DysonSchwinger results. Both classes of methods have access to condensates. Thus a comprehensive study of condensates becomes possible, in which I compare my calculations in holography and resummed field theory with each other, as well as with lattice results, field theory and experiment. I prove that the lowenergy theorems of QCD keep their validity in holographic models with a gluon condensate in a nontrivial way. I also show that the socalled decoupling relation holds in holography models with chiral and gluon condensates, whereas this relation fails in the DysonSchwinger approach. On the contrary, my results on the chiral magnetic effect in holography disagree with the weakfield prediction; the chiral magnetic effect (that is, the electric current generation in a magnetic field) is three times less than the current in the weaklycoupled QCD. The chiral condensate behavior is found to be quadratic in external field both in the DysonSchwinger approach and in holography, yet we know that in the exact limit the condensate must be linear, thus both classes of models are concluded to be deficient for establishing the correct condensate behaviour in the chiral limit. The magnetization of the QCD vacuum does not agree with the lattice data on chiral condensate magnetization; it is found to have a peculiar nonmonotonous dependence on the magnetic field, with a peak at some point, which cannot be explained so far. I speculate here that the peak might be related to the recently proposed electromagnetic superconductivity in QCD vacuum. Finally, I compare the quarkquark potential obtained from the holographic models and the potential obtained from the lattice to the potential I calculate via a combination of DysonSchwinger and EricsonSemenoffSzaboZarembo resummations. Apart from the perturbative Coulomb potential, I find confinement in the resummed theory; yet it is limited by a very short range and does not really allow us to go deeply in the infrared. This is interpreted as a signal of a very limited applicability of resummations to the deep infrared; on the contrary, holography yields robust and realistic results. When resummed nonlocal condensates are compared to known phenomenological values of nonlocality, the estimate for nonlocality of light quarks is wrong by several orders of magnitude, which again signalizes an inability of DysonSchwinger equations to describe correct physics in the infrared. Summing up these features of condensates, I must conclude that holography must be considered as a method to be used for IR physics {\it par excellence}, rather than DysonSchwinger equations. One could hope that in a few years at least the quarkscale electric fields will be feasible and some of the predictions of this work could be actually tested.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  QCD, strong fields, string theory, AdS/CFT correspondence, DysonSchwinger equations 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  17. January 2011 
1. Referee:  Erdmenger, Johanna 
Persistent Identifier (URN):  urn:nbn:de:bvb:19130747 
MD5 Checksum of the PDFfile:  51bcdfb4f7688c17a89c2728b5b3c3f5 
Signature of the printed copy:  0001/UMC 19459 
ID Code:  13074 
Deposited On:  19. May 2011 10:07 
Last Modified:  16. Oct 2012 08:50 