A conformal invariant growth model

We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption rates are local but the desorption rates are non-local; they depend not only on the cluster hit by the tile but also on the total number of peaks (local maxima) belonging to all the clusters of the configuration. The domain of the parameter is determined by the condition that the rates are non-negative. In the finite-size scaling limit, the model is conformal invariant in the whole open domain. The parameter appears in the sound velocity only. At the boundary of the domain, the stationary state is an adsorbing state and conformal invariance is lost. The model allows us to check the universality of non-local observables in the raise and peel model. An example is given.

Quantum current algebra for the AdS(5) x S(5) superstring

The sigma model describing the dynamics of the superstring in the AdS(5) x S(5) background can be constructed using the coset PSU(2, 2 vertical bar 4)/SO(4, 1) x SO(5). A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE`s is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE`s. We also compute the OPE`s of the left invariant currents with the energy momentum tensor at tree level and one loop.

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Fermion perturbations in string theory black holes

In this paper we study fermion perturbations in four-dimensional black holes of string theory, obtained either from a non-extreme configuration of three intersecting five-branes with a boost along the common string or from a non-extreme intersecting system of two two-branes and two five-branes. The Dirac equation for the massless neutrino field, after conformal re-scaling of the metric, is written as a wave equation suitable to study the time evolution of the perturbation. We perform a numerical integration of the evolution equation, and with the aid of Prony fitting of the time-domain profile, we calculate the complex frequencies that dominate the quasinormal ringing stage, and also determine these quantities by the semi-analytical sixth-order WKB method. We also find numerically the decay factor of fermion fields at very late times, and show that the falloff is identical to those showing for massless fields in other four-dimensional black hole spacetimes.