Stochastic processes with Z_N symmetry and complex Virasoro representations. The partition functions

In a previous Letter (J. Phys. A v.47 (2014) 212003) we have presented numerical evidence that a Hamiltonian expressed in terms of the generators of the periodic Temperley-Lieb algebra has, in the finite-size scaling limit, a spectrum given by representations of the Virasoro algebra with complex highest weights. This Hamiltonian defines a stochastic process with a Z_N symmetry. We give here analytical expressions for the partition functions for this system which confirm the numerics. For N even, the Hamiltonian has a symmetry which makes the spectrum doubly degenerate leading to two independent stochastic processes. The existence of a complex spectrum leads to an oscillating approach to the stationary state. This phenomenon is illustrated by an example.Comment: 8 pages, 4 figures, in a revised version few misprints corrected, one relevant reference adde

q_T Uncertainties for W and Z Production

Analysis of semi-inclusive DIS hadroproduction suggests broadening of transverse momentum distributions at small x below 1E-3 ~ 1E-2 which can be modeled in the Collins-Soper-Sterman formalism by a modification of impact parameter dependent parton densities. We investigate these consequences for the production of electroweak bosons at the Tevatron and the LHC. If substantial small-x broadening is observed in forward Z boson production in the Tevatron Run-2, it will strongly affect the predicted q_T distributions for W and Z boson production at the LHC.Comment: 4 pages, 2 figures; contribution to the XIII International Workshop on Deep Inelastic Scattering (DIS 2005

On the Ado Theorem for finite Lie conformal algebras with Levi decomposition

We prove that a finite torsion-free conformal Lie algebra with a splitting solvable radical has a finite faithful conformal representation.Comment: 11 page

Density profiles in the raise and peel model with and without a wall. Physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in a disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ($c = 0$ theory). We discover some unexpected values for the critical exponents, which were obtained using combinatorial methods. We have solved known (Pascal's hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting on their own since they give information on certain classes of alternating sign matrices.Comment: 39 pages, 28 figure

Gyratons on Melvin spacetime

We present and analyze new exact gyraton solutions of algebraic type II on a background which is static, cylindrically symmetric Melvin universe of type D. For a vanishing electromagnetic field it reduces to previously studied gyratons on Minkowski background. We demonstrate that the solutions are member of a more general family of the Kundt spacetimes. We show that the Einstein equations reduce to a set of mostly linear equations on a transverse 2-space and we discuss the properties of polynomial scalar curvature invariants which are generally non-constant but unaffected by the presence of gyratons.Comment: 15 pages, no figures, journal version extended by appendices B and