Affine Lie Algebra Symmetry of Sine-Gordon Theory at Reflectionless Points

The quantum affine symmetry of the sine-Gordon theory at q^2 = 1, which occurs at the reflectionless points, is studied. Conserved currents that correspond to the closure of simple root generators are considered, and shown to be local. We argue that they satisfy the affine sl(2) algebra. Examples of these currents are explicitly constructed.Comment: 8 pages, plaintex, uses harvma

Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve

We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the ``long-diagonal branes'' on the elliptic curve. We verify that they satisfy the relevant A-infinity consistency relations at both classical and quantum levels. In particular we find that the A-infinity relation for the annulus provides a reconstruction of annulus instantons out of disk instantons. We note in passing that the naive application of the Cardy-constraint does not hold for our correlators, confirming expectations. Moreover, we analyze various analytical properties of the correlators, including instanton flops and the mixing of correlators with different numbers of legs under monodromy. The classical and quantum A-infinity relations turn out to be compatible with such homotopy transformations. They lead to a non-invariance of the effective action under modular transformations, unless compensated by suitable contact terms which amount to redefinitions of the tachyon fields.Comment: 24 pages, 6 figures, LaTeX2

Supersymmetric Gelfand-Dickey Algebra

We study the classical version of supersymmetric $W$-algebras. Using the second Gelfand-Dickey Hamiltonian structure we work out in detail $W_2$ and $W_3$-algebras.Comment: 13 page

The Refined Elliptic Genus and Coulomb Gas Formulations of N=2N=2 Superconformal Coset Models

We describe, in some detail, a number of different Coulomb gas formulations of $N=2$ superconformal coset models. We also give the mappings between these formulations. The ultimate purpose of this is to show how the Landau-Ginzburg structure of these models can be used to extract the $W$-generators, and to show how the computation of the elliptic genus can be refined so as to extract very detailed information about the characters of component parts of the model.Comment: 40 pages in harvmac, no figure