André LeClair

String field theory on the conformal plane (I).: Kinematical Principles

We formulate string field theory geometrically by writing each term in the field theory action. as an expectation value in the 2-dimensional conformal field theory on the world surface. We show how the symmetries of the theory can be analyzed and the gauge invariance demonstrated from this point of view. As an application, we give a complete proof of the gauge invariance of Wittens open string field theory.

Quantum group symmetries and non-local currents in 2D QFT

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. TheS-matrices are completely characterized by these symmetries. FormalS-matrices for the imaginary-coupling affine Toda theories are thereby derived. The application of theseS-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 in 2d.

Fractional Supersymmetries in Perturbed Coset Cfts and Integrable Soliton Theory

Abstract We study integrable perturbations of the coset CFTs. The models are characterized by two fractional supersymmetries that are dual to each other. Generally, these models can be considered as restrictions of new integrable field theories we call fractional super soliton field theories. We study the connections with other models such as perturbations of WZW models, super sine-Gordon theory, Gross-Neveu models, and principal chiral models.

Boundary energy and boundary states in integrable quantum field theories

Abstract We study the ground-state energy of integrable 1 + 1 quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing 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 field, and also results for the energy, excited states and boundary S -matrix of O ( n ) and minimal models.

String field theory on the conformal plane (II).: Generalized Gluing

In our previous paper, we defined multistring vertices by conformally mapping string states onto the complex plane. In this paper, we prove the combination rules for these vertices. The contraction of two vertices by the natural inner product on the string Hilbert space yields just the composite vertex which would have been obtained by gluing together the two world sheets in an appropriate fashion.

Residual Quantum Symmetries of the Restricted {Sine-Gordon} Theories

Various aspects of the Restricted sine-Gordon (RSG) theories for the coupling β28π = pp+1 are examined. The particle spectrum is interpreted in terms of generalized kinks for the RSG potential, which is shown to effectively contain p−1 degenerate vacua. Simple arguments based on a study of the topological charge show that in the massless limit the RSG theories reduce to the Feigin-Fuchs construction. We find that the RSG S-matrices are characterized by a symmetry which generalizes supersymmetry to a fractional supersymmetry, and that the particles have fractional spin and statistics. In accordance with these results, we find some non-local chiral algebras in the minimal models that generalize the superconformal algebra, and whose currents are conserved in perturbation theory.

Restricted Sine-Gordon Theory and the Minimal Conformal Series

We make some observations that lend support to the following hypothesis: for special values of the sine-Gordon coupling constant, a truncation of the Hilbert space that preserves the integrability is possible, and these new theories have renormalization group fixed point behavior of a c<1 minimal conformal model. Our discussion centers on the method of quantum inverse scattering and its associated Yang-Baxter and quantum group structure.

The fractional supersymmetric sine-Gordon models

Abstract We define and study new integrable quantum field theories which we refer to as the fractional supersymmetric sine-Gordon theories. The field content consists of an interacting system of Z K parafermions and a boson. The modelsare characterized by a fractional supersymmetry. We find additional non-local conserved charges that can be identified with generators of the SU q (2) loop algebra. Exact S -matrices which are consistent with all of the symmetries are proposed. Special cases of the models include perturbations of the N =2 supersymmetric minimal series and current-current perturbations of the WZW models.

gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions

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 random-field 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 β-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 scale-invariant 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 sigma model whose target space is an analytic continuation of GL(N|N;C)/U(N|N), as well as its PSL(N|N) variant, and a corresponding generalized random XY model. For N=1 the sigma model is solved exactly and 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.

Purely transmitting defect field theories

Abstract We define an infinite class of integrable theories with a defect which are formulated as chiral defect perturbations of a conformal field theory. Such theories are massless in the bulk and are purely transmitting through the defect. The integrability of these theories requires the introduction of defect degrees of freedom. Such degrees of freedom lead to a novel set of Yang-Baxter equations. The defect degrees of freedom are identified through folding the chiral defect theories onto massless boundary field theories. The examples of the sine-Gordon theory and Ising model are worked out in some detail.