Restricted Quantum Affine Symmetry of Perturbed Minimal Models

We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed $\hat{sl(2)}$ affine Lie algebra symmetry of the sine-Gordon theory can be used to derive the S-matrices of the $\Phi^{(1,3)}$ perturbations of the minimal unitary series. This analysis provides an identification of fields which create the massive kink spectrum. We investigate the ultraviolet limit of the restricted sine-Gordon model, and explain the relation between the restriction and the Fock space cohomology of minimal models. We also comment on the structure of degenerate vacuum states. Deformed Serre relations are proven for arbitrary affine Toda theories, and it is shown in certain cases how relations of the Serre type become fractional spin supersymmetry relations upon restriction.Comment: 40 page

Errata for: Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point

We present some important corrections to our work which appeared in Nucl. Phys. B426 (1994) 534 (hep-th/9402144). Our previous results for the correlation functions $\langle e^{i\alpha \Phi(x)} e^{i\alpha' \Phi (0) } \rangle$ were only valid for $\alpha = \alpha'$, due to the fact that we didn't find the most general solution to the differential equations we derived. Here we present the solution corresponding to $\alpha \neq \alpha'$.Comment: 4 page

Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field Theory

Starting from a given S-matrix of an integrable quantum field theory in $1+1$ dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by introducing an adjoint action of the symmetry generators on fields, and specifying the form factors of descendents. The braiding relations of quantum field multiplets is shown to be given by the universal \CR-matrix. We develop in some detail the case of infinite dimensional Yangian symmetry. We show that the quantum double of the Yangian is a Hopf algebra deformation of a level zero Kac-Moody algebra that preserves its finite dimensional Lie subalgebra. The fields form infinite dimensional Verma-module representations; in particular the energy-momentum tensor and isotopic current are in the same multiplet.Comment: 29 page

On Ising Correlation Functions with Boundary Magnetic Field

Exact expressions of the boundary state and the form factors of the Ising model are used to derive differential equations for the one-point functions of the energy and magnetization operators of the model in the presence of a boundary magnetic field. We also obtain explicit formulas for the massless limit of the one-point and two-point functions of the energy operator.Comment: 19 pages, 5 uu-figures, macros: harvmac.tex and epsf.tex three references adde

Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models

We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with rotational spin of spin-1/2 particles. Since the spin-1/2 representation is not promoted to a representation of the Lorentz group, the model is not fully Lorentz invariant, although it has a relativistic dispersion relation. The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a unitary time evolution. Renormalization-group analysis shows the model has a low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed points. The critical exponents are computed to two-loop order. Possible applications to condensed matter physics in 3 space-time dimensions are discussed.Comment: v2: Published version, minor typose correcte

The Scattering Theory of Oscillator Defects in an Optical Fiber

We examine harmonic oscillator defects coupled to a photon field in the environs of an optical fiber. Using techniques borrowed or extended from the theory of two dimensional quantum fields with boundaries and defects, we are able to compute exactly a number of interesting quantities. We calculate the scattering S-matrices (i.e. the reflection and transmission amplitudes) of the photons off a single defect. We determine using techniques derived from thermodynamic Bethe ansatz (TBA) the thermodynamic potentials of the interacting photon-defect system. And we compute several correlators of physical interest. We find the photon occupancy at finite temperature, the spontaneous emission spectrum from the decay of an excited state, and the correlation functions of the defect degrees of freedom. In an extension of the single defect theory, we find the photonic band structure that arises from a periodic array of harmonic oscillators. In another extension, we examine a continuous array of defects and exactly derive its dispersion relation. With some differences, the spectrum is similar to that found for EM wave propagation in covalent crystals. We then add to this continuum theory isolated defects, so as to obtain a more realistic model of defects embedded in a frequency dependent dielectric medium. We do this both with a single isolated defect and with an array of isolated defects, and so compute how the S-matrices and the band structure change in a dynamic medium.Comment: 32 pages, TeX with harvmac macros, three postscript figure