International Journal of Modern Physics A

In the first part of this work we review the equations of motion for the brane presented in Friedmann–Robertson–Walker (FRW) form, when the bulk is five-dimensional (A)dS Black Hole. The spacelike (timelike) FRW brane equations are considered from the point of view of their representation in the form similar to two-dimensional CFT entropy, the so-called Cardy–Verlinde (CV) formula. The following five-dimensional gravities are reviewed: Einstein, Einstein–Maxwell and Einstein with brane quantum corrections. The second part of the work is devoted to the study of FRW brane equations and their representation in CV form, brane induced matter and brane cosmology in Einstein–Gauss–Bonnet (GB) gravity. In particular, we focus on the inflationary brane cosmology. The energy conditions for brane matter are also analyzed. We show that for some values of GB coupling constant (bulk is AdS BH) the brane matter is not CFT. Its energy density and pressure are not always positive. The appearance of logarithmic corrections in brane cosmology is discussed.

Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit N = ∞, where many properties can be analyzed analytically.

We calculate the low energy π π scattering lengths and , the coupling of the ρ to the pion g_{ρ π π}, the total width of the ρ, the low q² behavior of the pion electromagnetic form factor, and the pion scalar form factor within a chiral SU(2)_f NJL-type Lagrangian where the spin 1 ρ meson is generated from a four-quark tensor interaction. Such a simple model avoids the mathematical complication related to π - a₁ mixing. Two types of regularization are discussed, mainly affecting the values of and . We find rather good agreement with data. The ρ meson described in this way does not account for the meson vector dominance model: it does not contribute to the scattering lengths, and the charge radius of the pion is mainly ascribed to the bare photon quark coupling. Even if the shape of the electromagnetic form factor is well reproduced, the strong increase near the ρ pole does not account for the ρ→ππ decay but only reflects the structure of the ρ.

The form factors for the B→π transition are evaluated in the entire momentum transfer range by using the constraints obtained in the framework combining the heavy quark expansion and chiral symmetry for light quarks and the quark model. In particular, we calculate the valence quark contribution and show that it together with the equal time commutator contribution give to the form factors a pole behavior with the heavy (B-meson in our case) mass as the pole mass. This is in addition to the usual vector meson B*-pole diagram for B→πlν in the above framework. We discuss the predictions in our model, which provide an estimate of |V_ub|².

The free energy analyzed in the framework of the quantum field theory in conjunction with the statistical model for a meson is found to undergo an expansion in the condensate wave function. The superconducting and fractal properties of the meson are found to originate from the branch-cut type of singularity in the wave function of the model in which the gauge symmetry breaking is manifest.

The natural extension of Schwarzschild metric to the case of nonzero cosmological constant Λ known as the Kottler metric is considered and it is discussed under what circumstances the given metric could describe the Schwarzschild black hole immersed in a medium with nonzero energy density. Under the latter situation such an object might carry topologically inequivalent configurations of various fields. The given possibility is analyzed for complex scalar field and it is shown that the mentioned configurations might be tied with natural presence of Dirac monopoles on black hole under consideration. In turn, this could markedly modify the Hawking radiation process.