Supersymmetric Scattering in Two Dimensions

We briefly review results on two-dimensional supersymmetric quantum field theories that exhibit factorizable particle scattering. Our particular focus is on a series of $N\!=\!1$ supersymmetric theories, for which exact $S$-matrices have been obtained. A Thermodynamic Bethe Ansatz (TBA) analysis for these theories has confirmed the validity of the proposed $S$-matrices and has pointed at an interesting `folding' relation with a series of $N\!=\!2$ supersymmetric theories.Comment: 3 pages, wstwocl.sty, epsfig.sty, talk delivered at the HEP95 Conference of the EPS, Brussels, July/August 199

Tricritical Ising Model with a Boundary

We study the integrable and supersymmetric massive $\hat\phi_{(1,3)}$ deformation of the tricritical Ising model in the presence of a boundary. We use constraints from supersymmetry in order to compute the exact boundary $S$-matrices, which turn out to depend explicitly on the topological charge of the supersymmetry algebra. We also solve the general boundary Yang-Baxter equation and show that in appropriate limits the general reflection matrices go over the supersymmetry preserving solutions. Finally, we briefly discuss the possible connection between our reflection matrices and boundary perturbations within the framework of perturbed boundary conformal field theory

Conformal Invariance in (2+1)-Dimensional Stochastic Systems

Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and some are indeed proved) to be described by conformal field theories. We advance, in the framework of the Martin-Siggia-Rose field theoretical formalism of stochastic dynamics, a general solution of the translation Ward identities, which yields a putative conformal energy-momentum tensor. Even though the computation of energy-momentum correlators is obstructed, in principle, by dimensional reduction issues, these are bypassed by the addition of replicated fields to the original (2+1)-dimensional model. The method is illustrated with an application to the Kardar-Parisi-Zhang (KPZ) model of surface growth. The consistency of the approach is checked by means of a straightforward perturbative analysis of the KPZ ultraviolet region, leading, as expected, to its $c=1$ conformal fixed point.Comment: Title, abstract and part of the text have been rewritten. To be published in Physical Review E

Quantum Integrability of Certain Boundary Conditions

We study the quantum integrability of the O(N) nonlinear $\sigma$ (nls) model and the O(N) Gross-Neveu (GN) model on the half-line. We show that the \nls model is integrable with Neumann, Dirichlet and a mixed boundary condition, and that the GN model is integrable if \psi_+^a\x=\pm\psi_-^a\x. We also comment on the boundary condition found by Corrigan and Sheng for the O(3) nls model.Comment: 11 pages, Latex file, minor changes, one reference adde

Supersymmetric Reflection Matrices

We briefly review the general structure of integrable particle theories in 1+1 dimensions having N=1 supersymmetry. Examples are specific perturbed superconformal field theories (of Yang-Lee type) and the N=1 supersymmetric sine-Gordon theory. We comment on the modifications that are required when the N=1 supersymmetry algebra contains non-trivial topological charges.Comment: 7 pages, Revtex, 2 figures, talk given at the International Seminar on Supersymmetry and Quantum Field Theory, dedicated to the memory of D.V.Volkov, Kharkov (Ukraine), January 5-7, 199

Non-perturbative approach to backscattering off a dynamical impurity in 1D Fermi systems

We investigate the problem of backscattering off a time-dependent impurity in a one-dimensional electron gas. By combining the Schwinger-Keldysh method with an adiabatic approximation in order to deal with the corresponding out of equilibrium Dirac equation, we compute the total energy density (TED) of the system. We show how the free fermion TED is distorted by the backscattering amplitude and the geometry of the impurity.Comment: 5 pages, 2 figures, RevTex4. Appendix and some text added. Results and conclusions did not change. Version accepted for publication in Phys. Rev.