International Journal of Modern Physics A

We describe a method of solving quantum field theories using operator techniques based on the expansion of interacting fields in terms of asymptotic fields. For bound states, we introduce an asymptotic field for each (stable) bound state. We choose the nonrelativistic hydrogen atom as an example to illustrate the method. Future work will apply this N-quantum approach to relativistic theories that include bound states in motion.

We study the ηNN coupling constant using the method of QCD sum rules starting from the vacuum-to-eta correlation function of the interpolating fields of two nucleons. The matrix element of this correlation has been taken with respect to nucleon spinors to avoid unwanted pole contribution. The SU(3)-flavor symmetry breaking effects have been accounted for via the η-mass, s-quark mass and eta decay constant to leading order. Out of the four sum rules obtained by taking the ratios of the two sum rules in conjunction with the two sum rules in nucleon mass, three are found to give mutually consistent results. We find the SU(3) breaking effects significant, as large as 50% of the SU(3) symmetric part.

The aim of this paper is to present a connection between the Gribov–Zwanziger condition for the mass gap and spontaneous symmetry breaking. In order to clarify these relationship, a toy model is presented and some quantum aspects are discussed.

A nonperturbative model for the QCD invariant charge, which contains no low-energy unphysical singularities and possesses an elevated higher-loop corrections stability, is developed in the framework of potential approach. The static quark–antiquark potential is constructed by making use of the proposed model for the strong running coupling. The obtained result coincides with the perturbative potential at small distances and agrees with relevant lattice simulation data in the nonperturbative physically-relevant region. The developed model yields a reasonable value of the QCD scale parameter, which is consistent with its previous estimations obtained within potential approach.

Radiative neutrino mass models have interesting features, which make it possible to relate neutrino masses to the existence of dark matter. However, the explanation of the baryon number asymmetry in the universe seems to be generally difficult as long as we suppose leptogenesis based on the decay of thermal right-handed neutrinos. Since right-handed neutrinos are assumed to have masses of O(1) TeV in these models, they are too small to generate the sufficient lepton number asymmetry. Here we consider Affleck–Dine leptogenesis in a radiative neutrino mass model by using a famous flat direction LH_u as an alternative possibility. The constraint on the reheating temperature could be weaker than the ordinary models. The model explains all the origin of the neutrino masses, the dark matter, and also the baryon number asymmetry in the universe.

There is now motivating experimental evidence for relativistic symmetries in nuclei and hadrons, namely pseudospin and spin symmetry limits of the Dirac equation besides the old theoretical backgrounds. The most fundamental ingredients in such studies are definitely the wave functions and energy eigenvalues. Here, having in mind the importance of the Coulomb term as well as the degeneracy-removing role of tensor interaction, we obtain the exact solutions to the problem for Coulomb scalar, vector and tensor terms in both spin and pseudospin symmetry limits. We see that, contrary to many other common cumbersome techniques, the problem is simply solved via the methodology of supersymmetric quantum mechanics.

We study several types of classical rotating membrane solutions in AdS₄ ×Q^{1, 1, 1} and discuss their field theory duals. Q^{1, 1, 1} is a seven-dimensional Sasaki–Einstein manifold given as a nontrivial U(1) fibration over S²×S²×S², equipped with SU(2)³ ×U(1) isometry. It is recently suggested that there exist quiver Chern–Simons theories which are dual to M-theory in certain orbifolds of Q^{1, 1, 1}. The membrane solutions we consider have in general nonvanishing angular momenta both in AdS₄ and Q^{1, 1, 1} spaces. We present solutions for folded and wrapped membranes. According to the AdS/CFT correspondence, such classical solutions are dual to long operators of the dual conformal field theories in the large coupling limit. We analyze the asymptotic behaviour of the dispersion relation between energy (conformal dimension) and angular momenta (global charges).

We choose the mechanical action of open string in the presence of constant B-fields, which allows us to build up constraint structures. In an open string theory, the secondary constraints give rise to noncommutativity of the string coordinates on the boundaries. We find that applying the Batalin–Fradkin–Fradkina–Tyutin (BFFT) formalism to this noncommutative system converts it to a commutative one and makes new local gauge symmetries.

From BFSS matrix theory considerations, it is expected that a single D_p+2-brane action can be obtained from ND_p-brane action in large N limit. We examine and confirm this expectation by working out the details of DBI and Chern–Simons terms of D_p+2-brane action from D_p-brane action. We show that the same relation works for non-BPS, as well as BPS branes.

Cumulative observational evidence confirms that the surface gravity of dark matter (DM) halos μ_{0 D} = r₀ρ₀, where r₀ and ρ₀ are the halo core radius and central density, respectively, is nearly constant and independent of galaxy luminosity for a high number of galactic systems (spirals, dwarf irregular and spheroidals, elliptics) spanning over 14 magnitudes in luminosity and of different Hubble types. Remarkably, its numerical value, μ_0D ≃140M_⊙/pc² = (18.6 MeV)³, is approximately the same (up to a factor of 2) in all these systems. First, we present the physical consequences of the independence of μ_0D from r₀: the energy scales as the volume , while the mass and the entropy scale as the surface and the surface times log r₀, respectively. Namely, the entropy scales similarly to the black hole entropy but with a much smaller coefficient. Second, we compute the surface gravity and the density profile for small scales from first principles and the evolution of primordial density fluctuations from the end of inflation till today using the linearized Boltzmann–Vlasov equation. The density profile ρ_lin(r) obtained in this way decreases as r^-1-n_s/2 for intermediate scales, where n_s≃0.964 is the primordial spectral index. This scaling is in remarkable agreement with the empirical behavior found observationally and in N-body simulations: r^-1.6±0.4. The observed value of μ_0D indicates that the DM particle mass m is on the keV scale. The theoretically derived density profiles ρ_lin(r) turn to be cored for m on the keV scale and they are cusped for m on the GeV scale or beyond. We consider both fermions and bosons as DM particles decoupling either ultrarelativistically or nonrelativistically. Our results do not use any particle physics model and vary slightly with the statistics of the DM particle.

Inflationary potentials are investigated for specific models in type IIB string theory via flux compactification. As concrete models, we investigate several cases where the internal spaces are weighted projective spaces. The models we consider have two, three, or four Kähler moduli. The Kähler moduli play a role of inflaton fields and we consider the cases where only one of the moduli behaves as the inflaton field. For the cases with more than two moduli, we choose the diagonal basis for the expression of the Calabi–Yau volume, which can be written down as a function of four-cycle. With the combination of multiple moduli, we can express the multi-dimensional problem as an effective one-dimensional problem. In the large volume scenario, the potentials of these three models turn out to be of the same type. By taking the specific limit of the relation between the moduli and the volume, the potentials are reduced to simpler ones which induce inflation. For the case of two Kähler moduli, we exclude the potential as an inflationary model because the moduli might not be stable during inflation. As a toy model, we first consider the simple potential. We calculate the slow roll parameters ϵ, η and ξ for each inflationary potential. Then, we check whether the potentials give reasonable spectral indices n_s and their running α_s's by comparing with the recently released seven-year WMAP data. For both models, we see reasonable spectral indices for the number of e-folding 47<N_e<61. Conversely, by inserting the observed seven-year WMAP data, we see that the potential of the toy model gives requisite number of e-folds while the potential of the Kähler moduli gives much smaller number of e-folding. Finally, we see that two models do not produce reasonable values of the running of the spectral index.