International Journal of Modern Physics A

We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the worldvolume of a stack of D3-branes placed at the tip of a toric Calabi–Yau cone, at an "orbifold point" in Kähler moduli space. These provide an infinite class of four-dimensional superconformal field theories which may be studied in the context of the AdS/CFT correspondence. It is now understood that these gauge theories are completely specified by certain two-dimensional torus graphs, called brane tilings, and the combinatorics of the dimer models on these graphs. In particular, knowledge of the dual Sasaki–Einstein metric is not required to determine the gauge theory, only topological and symplectic properties of the toric Calabi–Yau cone. By analyzing the symmetries of the toric quiver theories we derive the dimer models and use them to construct the moduli space of the theory both classically and semiclassically. Using mirror symmetry the brane tilings are shown to arise in string theory on the worldvolumes of the fractional D6-branes that are mirror to the stack of D3-branes at the tip of the cone.

The possibility of deforming the (associative or Lie) product to obtain alternative descriptions for a given classical or quantum system has been considered in many papers. Here we discuss the possibility of obtaining some novel alternative descriptions by changing the linear structure instead. In particular we show how it is possible to construct alternative linear structures on the tangent bundle TQ of some classical configuration space Q that can be considered as "adapted" to the given dynamical system. This fact opens the possibility to use the Weyl scheme to quantize the system in different nonequivalent ways, "evading," so to speak, the von Neumann uniqueness theorem.

We perform a comprehensive analysis of the pion–photon transition form factor F_πγ(Q²) involving the transverse momentum corrections in the leading order approximation with the present CLEO experimental data, in which the contributions beyond the leading Fock state have been taken into consideration. As is well known, the leading Fock-state contribution dominates of F_πγ(Q²) at large momentum transfer (Q²) region. One should include the contributions beyond the leading Fock state in small Q² region. In this paper, we construct a phenomenological expression to estimate the contributions beyond the leading Fock state based on its asymptotic behavior at Q²→0. Our present theoretical results agree well with the experimental data in the whole Q² region. Then, we extract some useful information of the pionic leading twist-2 distribution amplitude (DA) by comparing our results of F_πγ(Q²) with the CLEO data. By taking best fit, we have the distribution amplitude moments, and all of higher moments, which are closed to the asymptotic-like behavior of the pion wave function.

The coherent hadron production analogous to Cherenkov radiation of photons gives rise to the ring-like events. Being projected on the ring diameter they produce the two-bump structure recently observed for the away-side jets at RHIC. The position of the peaks and their height determine such properties of the hadronic medium as its nuclear refractive index, the parton density, the free path length and the energy loss of Cherenkov gluons. Cherenkov gluons may be responsible for the asymmetry of dilepton mass spectra near ρ-meson observed in experiment. Beside comparatively low energy gluons observed at RHIC, there could be high energy gluons at LHC, related to the high energy region of positive real part of the forward scattering amplitude and possessing different characteristics. This would allow to scan (x, Q²)-plane determining the parton densities in its various regions.

The discovery of the jet quenching in central Au+Au collisions at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory has provided clear evidence for the formation of strongly interacting dense matter. It has been predicted to occur due to the energy loss of high energy partons that propagate through the quark–gluon plasma. In this paper we investigate the dependence of the parton energy loss due to elastic scatterings in a parton plasma on the value of the strong coupling and its running with the evolution of the system. We analyze different prescriptions for the QCD coupling and calculate the energy and length dependence of the fractional energy loss. Moreover, the partonic quenching factor for light and heavy quarks is estimated. We found that the predicted enhancement of the heavy to light hadrons (D/π) ratio is strongly dependent on the running of the QCD coupling constant.

The ground state wave function and the energy term of a relativistic electron moving in the field of two fixed centers, when interaction of this particle with centers is described by two Coulomb and two Coulomb-like scalar potentials are calculated analytically by the LCAO method. Dependence of electron binding energy from value of scalar coupling constant was investigated using obtained analytic results.

The summation of the partial wave series for Coulomb scattering amplitude, f^C(θ) is usually avoided because the series is oscillatorily and divergent. Instead, f^C(θ) is generally obtained by solving the Schrödinger equation in parabolic cylindrical coordinates which is not a general method. Here, we show that a reconstructed series, (1-cos θ)²f^C(θ), is both convergent and analytically summable.

In loop quantum cosmology nonperturbative modification to a scalar matter field at short scales implies inflation which also means a violation of the strong energy condition. In the framework of effective Hamiltonian we discuss the issue of violation of the strong energy condition in the presence of quantum geometry potential. It is shown that the appearance of quantum geometry potential strengthens the violation of the strong energy condition in small volume regions. In the small volume regions superinflation can easily happen. Furthermore, when the evolution of the universe approaches the bounce scale, this trend of violating the strong energy condition can be greatly amplified.