Towards Baxter equation in supersymmetric Yang-Mills theories

We perform an explicit two-loop calculation of the dilatation operator acting on single trace Wilson operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in N=2 and N=4 supersymmetric Yang-Mills theories. We demonstrate that its eigenspectrum exhibits double degeneracy of opposite parity eigenstates which suggests that the two-loop dilatation operator is integrable. Moreover, the two-loop anomalous dimensions in the two theories differ from each other by an overall normalization factor indicating that the phenomenon is not sensitive to the presence of the conformal symmetry. Relying on these findings, we try to uncover integrable structures behind the two-loop dilatation operator using the method of the Baxter Q-operator. We propose a deformed Baxter equation which exactly encodes the spectrum of two-loop anomalous dimensions and argue that it correctly incorporates a peculiar feature of conformal scalar operators -- the conformal SL(2) spin of such operators is modified in higher loops by an amount proportional to their anomalous dimension. From the point of view of spin chains this property implies that the underlying integrable model is ``self-tuned'' -- the all-loop Hamiltonian of the spin chain depends on the total SL(2) spin which in its turn is proportional to the Hamiltonian.Comment: Latex, 18 pages, 3 figure

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with compact spatial sections of negative spatial curvature.Comment: 10 pages. Contribution to the "Fifth Alexander Friedmann International Seminar on Gravitation and Cosmology," Joao Pessoa, Brazil, 2002. Revised version, with altered Abstract and one new referenc

Anisotropic magnetic behavior of GdBa_2Cu_3O_{6+y} single crystals

Magnetic properties of high-quality Al-free nonsuperconducting GdBa_2Cu_3O_{6+y} single crystals grown by flux method have been studied. The magnetic anisotropy below the N\'eel temperature T_N~2.3K corresponds to the direction of Gd^{3+} magnetic moments along the tetragonal c-axis. At T < T_N clear indications of spin-flop transitions for H||c have been observed on magnetization curves at H_{sf}~10kOe. Magnetic phase diagrams have been obtained for H||c as well as for H||ab. A pronounced anisotropy in the magnetic susceptibility (unexpected for Gd-based compounds) has been found above T_N.Comment: 2 pages, 3 figures; LT23 (Aug. 2002; Hiroshima), accepted to Physica

Collision of Viscoelastic Spheres: Compact Expressions for the Coefficient of Normal Restitution

The coefficient of restitution of colliding viscoelastic spheres is analytically known as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While beeing analytically exact, this result is not suitable for applications in efficient event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on the analytic result, here we derive expressions for the coefficient of restitution which allow for an application in efficient eMD and MC simulations of granular Systems.Comment: 4 pages, 4 figure

On the interrelation between monopoles, vortices, topological charge and chiral symmetry breaking: an analysis using overlap fermions for SU(2)

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q_{index}=0. The remaining (ultraviolet) monopoles without vortices and -- to a less extent -- the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.Comment: 13 pages, 5 figures, strongly revised, results added, one figure added, accepted for publication, title changed

Efficiency of different matrix inversion methods applied to Wilson fermions

We compare different conjugate gradient -- like matrix inversion methods (CG, BiCGstab1 and BiCGstab2) employing for this purpose the compact lattice quantum electrodynamics (QED) with Wilson fermions. The main goals of this investigation are the CPU time efficiency of the methods as well as the influence of machine precision on the reliability of (physical) results especially close to the 'critical' line ~\kappa_c(\bt).Comment: 27 pages LaTeX (epsf), all figures include