Vector Multiplets and the Phases of N = 2 Theories in 2D Through the Looking Glass

We extend Witten's discussion of actions related to the Landau-Ginzburg description of Calabi-Yau hypersurfaces in weighted projective spaces to cover the mirror class of models that include twisted chiral matter multiplets and a newly discovered 2D, N = 2 twisted vector multiplet. Certain integrability obstructions are observed that constrain the most general constructions containing both matter and twisted matter simultaneously. It is conjectured that knot invariants will ultimately play a role in describing the most general such model.Comment: 11 page

Loop equations for the semiclassical 2-matrix model with hard edges

The 2-matrix models can be defined in a setting more general than polynomial potentials, namely, the semiclassical matrix model. In this case, the potentials are such that their derivatives are rational functions, and the integration paths for eigenvalues are arbitrary homology classes of paths for which the integral is convergent. This choice includes in particular the case where the integration path has fixed endpoints, called hard edges. The hard edges induce boundary contributions in the loop equations. The purpose of this article is to give the loop equations in that semicassical setting.Comment: Latex, 20 page

Coulomb gas representation of quantum Hall effect on Riemann surfaces

Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy.Comment: 10 pages, LaTex, the paper is completely rewritten, It will be appeared in : Jour. Phys. A 32 (1999