On String S-matrix, Bound States and TBA

The study of finite J effects for the light-cone AdS superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The S-matrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror S-matrix fixes the S-matrices of both theories essentially uniquely. The resulting string S-matrix S(z_1,z_2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2^{M-1} solutions of the M-particle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they might receive a finite J correction to their energy which is complex, or the energy correction might exceed corrections arising due to finite J modifications of the Bethe equations thus making the asymptotic Bethe ansatz inapplicable.Comment: 77 pages, 6 figures, v2: the statement about the periodicity condition for mirror fermions corrected; typos corrected; references added, v3: misprints correcte

q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit

A set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra su(2|2). The S-matrices are a function of two independent couplings g and q=exp(i\pi/k). The main result is to find the scalar factor, or dressing phase, which ensures that the unitarity and crossing equations are satisfied. For generic (g,k), the S-matrices are branched functions on a product of rapidity tori. In the limit k->infinity, one of them is identified with the S-matrix describing the magnon excitations on the string world sheet in AdS5 x S5, while another is the mirror S-matrix that is needed for the TBA. In the g->infinity limit, the rapidity torus degenerates, the branch points disappear and the S-matrices become meromorphic functions, as required by relativistic S-matrix theory. However, it is only the mirror S-matrix which satisfies the correct relativistic crossing equation. The mirror S-matrix in the relativistic limit is then closely related to that of the semi-symmetric space sine-Gordon theory obtained from the string theory by the Pohlmeyer reduction, but has anti-symmetric rather than symmetric bound states. The interpolating S-matrix realizes at the quantum level the fact that at the classical level the two theories correspond to different limits of a one-parameter family of symplectic structures of the same integrable system.Comment: 41 pages, late

On the Disappearance of the Broad-Line Region in Low-Luminosity Agns

The disk-wind scenario for the broad-line region (BLR) and toroidal obscuration in active galactic nuclei predicts the disappearance of the BLR at low luminosities. In accordance with the model predictions, data from a nearly complete sample of nearby AGNs show that the BLR disappears at luminosities lower than 5\times\E{39} (M/10^7\Mo)^{2/3} erg s^{-1), where $M$ is the black hole mass. The radiative efficiency of accretion onto the black hole is \la \E{-3} for these sources, indicating that their accretion is advection-dominated.Comment: ApJ Letters, to be publishe

From the Circumnuclear Disk in the Galactic Center to thick, obscuring tori of AGNs

We compare three different models of clumpy gas disk and show that the Circumnuclear Disk (CND) in the Galactic Center and a putative, geometrically thick, obscuring torus are best explained by a collisional model consisting of quasi-stable, self-gravitating clouds. Kinetic energy of clouds is gained by mass inflow and dissipated in cloud collisions. The collisions give rise to a viscosity in a spatially averaged gas dynamical picture, which connects them to angular momentum transport and mass inflow. It is found that CND and torus share the same gas physics in our description, where the mass of clouds is 20 - 50 M_sun and their density is close to the limit of disruption by tidal shear. We show that the difference between a transparent CND and an obscuring torus is the gas mass and the velocity dispersion of the clouds. A change in gas supply and the dissipation of kinetic energy can turn a torus into a CND-like structure and vice versa. Any massive torus will naturally lead to sufficiently high mass accretion rates to feed a luminous AGN. For a geometrically thick torus to obscure the view to the center even super-Eddington accretions rates with respect to the central black hole are required.Comment: 9 pages, no figures. Accepted for publication in A&