Twisted Quantum Affine Superalgebra Uq[gl(m∣n)(2)]U_q[gl(m|n)^{(2)}] and New Uq[osp(m∣n)]U_q[osp(m|n)] Invariant R-matrices

The minimal irreducible representations of $U_q[gl(m|n)]$, i.e. those irreducible representations that are also irreducible under $U_q[osp(m|n)]$ are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra $U_q[gl(m|n)^{(2)}]$. The $U_q[osp(m|n)]$ invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from $U_q[gl(m|n)^{(2)}]$, which exhibit novel features not previously seen in the untwisted or non-super cases.Comment: 19 pages, Latex fil

Exact S-Matrices for Nonsimply-Laced Affine Toda Theories

We derive exact, factorized, purely elastic scattering matrices for affine Toda theories based on the nonsimply-laced Lie algebras and superalgebras.Comment: 38 page

Exact S-Matrices with Affine Quantum Group Symmetry

We show how to construct the exact factorized S-matrices of 1+1 dimensional quantum field theories whose symmetry charges generate a quantum affine algebra. Quantum affine Toda theories are examples of such theories. We take into account that the Lorentz spins of the symmetry charges determine the gradation of the quantum affine algebras. This gives the S-matrices a non-rigid pole structure. It depends on a kind of ``quantum'' dual Coxeter number which will therefore also determine the quantum mass ratios in these theories. As an example we explicitly construct S-matrices with $U_q(c_n^{(1)})$ symmetry.Comment: Latex file, 21 page

G_2^1 Affine Toda Field Theory: A Numerical Test of Exact S-Matrix results

We present the results of a Monte--Carlo simulation of the $G_2^{(1)}$ Affine Toda field theory action in two dimensions. We measured the ratio of the masses of the two fundamental particles as a function of the coupling constant. Our results strongly support the conjectured duality with the $D_4^{(3)}$ theory, and are consistent with the mass formula of Delius et al.Comment: 5 pages, LaTeX, DTP-9223, DAMTP-92-4

Restricting affine Toda theory to the half-line

We restrict affine Toda field theory to the half-line by imposing certain boundary conditions at $x=0$. The resulting theory possesses the same spectrum of solitons and breathers as affine Toda theory on the whole line. The classical solutions describing the reflection of these particles off the boundary are obtained from those on the whole line by a kind of method of mirror images. Depending on the boundary condition chosen, the mirror must be placed either at, in front, or behind the boundary. We observe that incoming solitons are converted into outgoing antisolitons during reflection. Neumann boundary conditions allow additional solutions which are interpreted as boundary excitations (boundary breathers). For $a_n^{(1)}$ and $c_n^{(1)}$ Toda theories, on which we concentrate mostly, the boundary conditions which we study are among the integrable boundary conditions classified by Corrigan et.al. As applications of our work we study the vacuum solutions of real coupling Toda theory on the half-line and we perform semiclassical calculations which support recent conjectures for the $a_2^{(1)}$ soliton reflection matrices by Gandenberger.Comment: 39 pages, 4 ps figure

Exact s-Matrices for the Nonsimply-Laced Affine Toda Theories a2n−1(2)a_{2n-1}^{(2)}

We derive the exact, factorized, purely elastic scattering matrices for the $a_{2n-1}^{(2)}$ family of nonsimply-laced affine Toda theories. The derivation takes into account the distortion of the classical mass spectrum by radiative correction, as well as modifications of the usual bootstrap assumptions since for these theories anomalous threshold singularities lead to a displacement of some single particle poles.Comment: 11 page

Quantum Conserved Currents in Affine Toda Theories

We study the renormalization and conservation at the quantum level of higher-spin currents in affine Toda theories with particular emphasis on the nonsimply-laced cases. For specific examples, namely the spin-3 current for the $a_3^{(2)}$ and $c_2^{(1)}$ theories, we prove conservation to all-loop order, thus establishing the existence of factorized S-matrices. For these theories, as well as the simply-laced $a_2^{(1)}$ theory, we compute one-loop corrections to the corresponding higher-spin charges and study charge conservation for the three-particle vertex function. For the $a_3^{(2)}$ theory we show that although the current is conserved, anomalous threshold singularities spoil the conservation of the corresponding charge for the on-shell vertex function, implying a breakdown of some of the bootstrap procedures commonly used in determining the exact S-matrix.Comment: 19 page