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