International Journal of Modern Physics A

We review the main aspects of the warm inflation scenario, focusing on the inflationary dynamics and the predictions related to the primordial spectrum of perturbations, to be compared with the recent cosmological observations. We study in detail three different classes of inflationary models, chaotic, hybrid models and hilltop models, and discuss their embedding into supersymmetric models and the consequences for model building of the warm inflationary dynamics based on first principles calculations. Due to the extra friction term introduced in the inflaton background evolution generated by the dissipative dynamics, inflation can take place generically for smaller values of the field, and larger values of couplings and masses. When the dissipative dynamics dominates over the expansion, in the so-called strong dissipative regime, inflation proceeds with sub-Planckian inflaton values. Models can be naturally embedded into a supergravity framework, with SUGRA corrections suppressed by the Planck mass now under control, for a larger class of Kähler potentials. In particular, this provides a simpler solution to the "eta" problem in supersymmetric hybrid inflation, without restricting the Kähler potentials compatible with inflation. For chaotic models dissipation leads to a smaller prediction for the tensor-to-scalar ratio and a less tilted spectrum when compared to the cold inflation scenario. We find in particular that a small component of dissipation renders the quartic model now consistent with the current CMB data.

In this paper, we try to provide a direct method for calculating quark number susceptibility at finite chemical potential and zero temperature. In our approach, quark number susceptibility is totally determined by G[μ](p) (the dressed quark propagator at finite chemical potential μ). By applying the general result given in Phys. Rev. C71, 015205 (2005), G[μ](p) is calculated from the model quark propagator proposed in Phys. Rev. D67, 054019 (2003). From this the full analytic expression of quark number susceptibility at finite μ and zero T is obtained.

It has been argued that Nekrasov's partition function gives the generating function of refined BPS state counting in the compactification of M theory on local Calabi–Yau spaces. We show that a refined version of the topological vertex we previously proposed (arXiv:hep-th/0502061) is a building block of Nekrasov's partition function with two equivariant parameters. Compared with another refined topological vertex by Iqbal, Kozcaz and Vafa (arXiv:hep-th/0701156), our refined vertex is expressed entirely in terms of the specialization of the Macdonald symmetric functions which is related to the equivariant character of the Hilbert scheme of points on ℂ². We provide diagrammatic rules for computing the partition function from the web diagrams appearing in geometric engineering of Yang–Mills theory with eight supercharges. Our refined vertex has a simple transformation law under the flop operation of the diagram, which suggests that homological invariants of the Hopf link are related to the Macdonald functions.

It is shown that the four quantum trefoil solitons that are described by the irreducible representations of the quantum algebra SL_q(2) [and that may be identified with the four families of elementary fermions (e, μ, τ; ν_eν_μν_τ;d, s, b; u, c, t)] may be built out of three preons, chosen from two charged preons with charges (1/3, -1/3) and two neutral preons. These preons are fermions and are described by the representation of SL_q(2). There are also four bosonic preons described by the and representations of SL_q(2). The knotted standard theory may be replicated at the preon level and the conjectured particles are in principle indirectly observable.

We investigate the classical evolution of a ϕ⁴ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a noninteger mass dimension. These configurations resemble the equilibrium state of a critical scalar condensate. The measures of the initial fractal behavior vary in time following the mean field motion. We show that the remnants of the original fractal geometry survive and leave an imprint in the system time averaged observables, even for large times compared to the approximate oscillation period of the mean field, determined by the model parameters. This behavior becomes more transparent in the evolution of a deterministic Cantor-like scalar field configuration. We extend our study to the case of two interacting scalar fields, and we find qualitatively similar results. Therefore, our analysis indicates that the geometrical properties of a critical system initially at equilibrium could sustain for several periods of the field oscillations in the phase of nonequilibrium evolution.

The radiative leptonic decays D_s → μν_μγ and D → μν_μγ are investigated at the tree level within the relativistic independent quark model based on the confining potential in the scalar–vector harmonic form. The branching ratios for these decays in the vanishing lepton mass limit are obtained as ℬr(D_s → μν_μγ) = 4.94×10^-4 and ℬr(D → μν_μγ) = 3.34×10^-5, which includes the contributions of the internal bremsstrahlung and structure dependent diagrams at the level of the quark constituents. Finally, the photon energy spectra as predicted here is found to be symmetric about the peak value of the photon energy at .

The mass of the Kaluza–Klein black holes is investigated by means of the thermodynamic potential and the Hawking–Horowitz mass. It is pointed out that the mass estimated from the thermodynamic potential agrees with the Hawking–Horowitz mass. The mass of the limiting cases of the Kaluza–Klein black holes is discussed.