We construct and study the implications of some new non-local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions, including the sine-Gordon theory and its generalization to affine Toda theory. These non-local currents provide a non-perturbative formulation of the theories. The symmetry algebras correspond to the quantum affine Kac-Moody algebras. The S-matrices are completely characterized by these symmetries. Formal 5-matrices for the imaginary-coupling affine Toda theories are thereby derived. The application of these 5-matrices to perturbed coset conformal field theory is studied. Non-local charges generating the finite dimensional Quantum Group in the Liouville theory are briefly presented. The formalism based on non-local charges we describe provides an algernative to the quantum inverse scattering method for solving integrable quantum field theories in2d.

Finite temperature correlation functions in integrable quantum field theories are formulated only in terms of the usual, temperature-independent form factors, and certain thermodynamic filling fractions which are determined from the thermodynamic Bethe ansatz. Explicit expressions are given for the one and two-point functions.Typeset using REVT E Xwhere S A,A 1 are S-matrix factors required to bring |A into the order |A 2 , A 1 , i.e. A| = S A,A 1 A 2 , A 1 |, and similarly for |B . The inner products A 2 |B 2 are most easily evaluated by introducing free particle creation-annihilation operators |θ 1 · · · θ n = A † (θ 1 ) · · · A † (θ n )|0 , 1 In this paper we consider only "fermionic" theories with S(θ = 0) = −1. The formal extension to bosonic theories with S(θ = 0) = 1 is a simple exercise.

We consider the non-hermitian 2D Dirac Hamiltonian with (A): real random mass, imaginary scalar potential and imaginary gauge field potentials, and (B): arbitrary complex random potentials of all three kinds. In both cases this Hamiltonian gives rise to a delocalization transition at zero energy with particle-hole symmetry in every realization of disorder. Case (A) is in addition time-reversal invariant, and can also be interpreted as the randomfield XY Statistical Mechanics model in two dimensions. The supersymmetric approach to disorder averaging results in current-current perturbations of gl(N |N ) super-current algebras. Special properties of the gl(N |N ) algebra allow the exact computation of the βeta-functions, and of the correlation functions of all currents. One of them is the Edwards-Anderson order parameter. The theory is 'nearly conformal' and possesses a scaleinvariant subsector which is not a current algebra. For N = 1, in addition, we obtain an exact solution of all correlation functions. We also study the delocalization transition of case (B), with broken time reversal symmetry, in the Gade-Wegner (Random-Flux) universality class, using a GL(N |N ; C)/U (N |N ) sigma model, as well as its P SL(N |N ) variant, and a corresponding generalized random XY model. For N = 1 the sigma model is shown to be identical to the current-current perturbation. For the delocalization transitions (case (A) and (B)) a density of states, diverging at zero energy, is found.

W e study the ground state energy of integrable 1+1 quantum eld theories with boundaries (the genuine Casimir eect). In the scalar case, this is done by i n troducing a new, \R-channel TBA", where the boundary is represented by a boundary state, and the thermodynamics involves evaluating scalar products of boundary states with all the states of the theory. In the non-scalar, sine-Gordon case, this is done by generalizing the method of Destri and De Vega. The two approaches are compared. Miscellaneous other results are obtained, in particular formulas for the overall normalization and scalar products of boundary states, exact partition functions for the critical Ising model in a boundary magnetic eld, and also results for the energy, excited states and boundary S-matrix of O(n) and minimal models. 3/95

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