Boundary One-Point Functions, Scattering, and Background Vacuum Solutions in Toda Theories

The parametric families of integrable boundary affine Toda theories are considered. We calculate boundary one-point functions and propose boundary S-matrices in these theories. We use boundary one-point functions and S-matrix amplitudes to derive boundary ground state energies and exact solutions describing classical vacuum configurations.Comment: 20 pages, LaTe

Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.Comment: 12 pages, 1 figure, amslatex, bibtex (added missing label eq.11

Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page

Spin chains with dynamical lattice supersymmetry

Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the N=(2,2) superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension admits a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured.Comment: Revised version, 52 pages, 2 figure

An eigenvalue problem related to the non-linear sigma-model: analytical and numerical results

An eigenvalue problem relevant for the non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime (large R) the eigenvalues admit a power series expansion around the IR critical point R --> infinity. We compute high order coefficients and prove that the series converges for all finite values of R. In the ultraviolet (UV) limit the spectrum condenses into a continuum spectrum with a set of residual bound states. The spectrum agrees nicely with the central charge computed by the thermodynamic Bethe ansatz method