Zayakin, Andrey (2011): Properties of the Vacuum in Models for QCD: Holography vs. Resummed Field Theory. A Comparative Study. Dissertation, LMU München: Fakultät für Physik
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 non-pertubative 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 non-perturbative features of the theory. Archetypal examples of a non-perturbative parameter in QCD are gluon condensate and quark condensate. Condensates enter into many low-energy observables and thus are directly experiment-related. On the other hand, the power of modern experimental laser-physics 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 model-building 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 so-called 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 higher-dimensional theory. The advantage of the holographic models is that they render a strongly-coupled four-dimensional gauge theory as a dual of some weakly-coupled 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 real-life 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 viscosity-to-entropy 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, Dyson--Schwinger equations first of all. Non-local 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 Dyson--Schwinger 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 low-energy theorems of QCD keep their validity in holographic models with a gluon condensate in a non-trivial way. I also show that the so-called decoupling relation holds in holography models with chiral and gluon condensates, whereas this relation fails in the Dyson--Schwinger approach. On the contrary, my results on the chiral magnetic effect in holography disagree with the weak-field prediction; the chiral magnetic effect (that is, the electric current generation in a magnetic field) is three times less than the current in the weakly-coupled QCD. The chiral condensate behavior is found to be quadratic in external field both in the Dyson--Schwinger 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 non-monotonous 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 quark-quark potential obtained from the holographic models and the potential obtained from the lattice to the potential I calculate via a combination of Dyson--Schwinger and Ericson--Semenoff--Szabo--Zarembo 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 non-local condensates are compared to known phenomenological values of non-locality, the estimate for non-locality of light quarks is wrong by several orders of magnitude, which again signalizes an inability of Dyson--Schwinger 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 Dyson--Schwinger equations. One could hope that in a few years at least the quark-scale electric fields will be feasible and some of the predictions of this work could be actually tested.