Volume 200, Nº 3 (2019)

The Skyrme-Faddeev model has planar soliton solutions with the target space ℂP^N. An Abelian Chern-Simons term (the Hopf term) in the Lagrangian of the model plays a crucial role for the statistical properties of the solutions. Because П₃(ℂP¹) = ℤ, the term becomes an integer for N = 1. On the other hand, for N > 1, it becomes perturbative because П₃(ℂP^N) is trivial. The prefactor Θ of the Hopf term is not quantized, and its value depends on the physical system. We study the spectral flow of normalizable fermions coupled with the baby-Skyrme model (ℂP^N Skyrme-Faddeev model). We discuss whether the statistical nature of solitons can be explained using their constituents, i.e., quarks.

We calculate the strongly intensive variables Σ and Δ that suppress trivial volume fluctuations and are constructed for the charged particle multiplicity n and the total transverse momentum P_t in a modified multipomeron exchange approach for proton-proton interactions in the range of collision energies attainable with the SPS and LHC accelerators. In this approach, the interaction between the color quark-gluon strings formed from cut pomerons are effectively taken into account; in this case, the role of these interactions increases as the collision energy increases. The inequalities Σ(P_t, n) > 1 and Δ(P_t, n) < 1, which agree with the experimental data, are the main result of the calculations for energies attainable at the SPS. We show that as the energy increases, Σ(P_t, n) behaves nonmonotonically and Δ(P_t, n) increases.

We briefly review recent applications of holographic renormalization group flow equations in a hot and dense quark-gluon plasma (QGP). We especially focus on presenting a few examples typically used in the holographic description of the QGP. We study the influence of the chemical potential on the holographic β-function in these examples.

We study an instructive model of the directed percolation process near its second-order phase transition between absorbing and active states. We first express the model as a Langevin equation and then rewrite it in a field theory formulation. Using the Feynman diagram technique and the perturbative renormalization group method, we then analyze the resulting response functional. The percolation process is assumed to occur in an external velocity field, which has an additional effect on the properties of spreading. We use the Kraichnan rapid-change ensemble to generate velocity fluctuations. We obtain the structure of the set of fixed points in the two-loop approximation.

We construct a quantum kinetic theory of a weakly interacting critical boson gas using the expectation values of products of Heisenberg field operators in the grand canonical ensemble. Using a functional representation for the Wick theorem for time-ordered products, we construct a perturbation theory for the generating functional of these time-dependent Green’s functions at a finite temperature. We note some problems of the functional-integral representation and discuss unusual apparent divergences of the perturbation expansion. We propose a regularization of these divergences using attenuating propagators. Using a linear transformation to variables with well-defined scaling dimensions, we construct an infrared effective field theory. We show that the structure of the regularized model is restored by renormalization. We propose a multiplicatively renormalizable infrared effective model of the quantum dynamics of a boson gas.

We study various methods for estimating the deconfinement temperature in nondynamical bottom-up AdS/QCD models in detail. We show that although there are many different possibilities to define the holographic parameters, certain reasonable theoretical and phenomenological restrictions on holographic models lead to realistic and rather stable predictions for the range of temperatures in the deconfinement crossover region at small baryon densities. In particular, we argue that the most successful approach is to take the scalar glueball trajectory from lattice simulations as a basic input in an improved version of the soft-wall holographic model.