THE (0,2) EXACTLY SOLVABLE STRUCTURE OF CHIRAL RINGS, LANDAU-GINZBURGTHEORIES AND CALABI-YAU MANIFOLDS

We identify the exactly solvable theory of the conformal fixed point o f (0,2) Calabi-Yau sigma-models and their Landau-Ginzburg phases. To t his end we consider a number of (0,2) models constructed from a partic ular (2,2) exactly solvable theory via the method of simple currents. In order to establish the relation between exactly solvable (0,2) vacu a of the heterotic string, (0,2) Landau-Ginzburg orbifolds and (0,2) C alabi-Yau manifolds, we compute the Yukawa couplings of the exactly so lvable model and compare the results with the product structure of the chiral ring which we extract from the structure of the massless spect rum of the exact theory. We find complete agreement between the two up to a finite number of renormalizations. For a particularly simple exa mple we furthermore derive the generating ideal of the chiral ring fro m a (0,2) linear sigma-model which has both a Landau-Ginzburg and a (0 ,2) Calabi-Yau phase.