Notes on WGLnWGL_n-Algebras and Quantum Miura Transformation

We start from the quantum Miura transformation [7] for the $W$-algebra associated with $GL(n)$ group and find an evident formula for quantum L-operator as well as for the action of $W_l$ currents (l=1,..,n) on elements of the completely degenerated n-dimensional representation. Quantum formulae are obtained through the deformation of the pseudodifferential symbols. This deformation is independent of $n$ and preserves Adler's trace. Our main instrument of the proof is the notation of pseudodifferential symbol with right action which has no counterpart in classical theory.Comment: Landau-tmp-4-93, 15 pages, Tex (vanilla.sty

Quantum noncommutative ABJM theory: first steps

We introduce ABJM quantum field theory in the noncommutative spacetime by using the component formalism and show that it is N=6 supersymmetric. For the U(1)_{\kappa} x U(1)_{-\kappa} case, we compute all one-loop 1PI two and three point functions in the Landau gauge and show that they are UV finite and have well-defined commutative limits theta^{\mu\nu} -> 0, corresponding exactly to the 1PI functions of the ordinary ABJM field theory. This result also holds for all one-loop functions which are UV finite by power counting. It seems that the quantum noncommutative ABJM field theory is free from the noncommutative IR instabilities.Comment: 43 pages and 25 figures, corrected trivial typos, misprints, misplaced symbols et

Crossover critical behavior in the three-dimensional Ising model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussedComment: 10 pages in two-column format including 9 figures and 1 table. Submitted to J. Stat. Phys. in honor of M. E. Fisher's 70th birthda

Role of Landau-Rabi quantization of electron motion on the crust of magnetars within the nuclear energy density functional theory

Magnetic fields of order $10^{15}$ G have been measured at the surface of some neutron stars, and much stronger magnetic fields are expected to be present in the solid region beneath the surface. The effects of the magnetic field on the equation of state and on the composition of the crust due to Landau-Rabi quantization of electron motion are studied. Both the outer and inner crustal regions are described in a unified and consistent way within the nuclear-energy density functional theory.Comment: 23 pages, 11 figure

Role of center vortices in chiral symmetry breaking in SU(3) gauge theory

We study the behavior of the AsqTad quark propagator in Landau gauge on SU(3) Yang-Mills gauge configurations under the removal of center vortices. In SU(2) gauge theory, center vortices have been observed to generate chiral symmetry breaking and dominate the infrared behavior of the quark propagator. In contrast, we report a weak dependence on the vortex content of the gauge configurations, including the survival of dynamical mass generation on configurations with vanishing string tension.Comment: 8 pages, 9 figure

Anisotropic hypoelliptic estimates for Landau-type operators

We establish global hypoelliptic estimates for linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations, we establish for linear Landau-type operators optimal global hypoelliptic estimates with loss of 4/3 derivatives in a Sobolev scale which is exactly related to the anisotropy of the diffusion.Comment: 44 page