Singlet Couplings and (0,2) Models

We use the quantum symmetries present in string compactification on Landau-Ginzburg orbifolds to prove the existence of a large class of exactly marginal (0,2) deformations of (2,2) superconformal theories. Analogous methods apply to the more general (0,2) models introduced in \DK, lending further credence to the fact that the corresponding \LG\ models represent bona-fide (0,2) SCFTs. We also use the large symmetry groups which arise when the worldsheet superpotential is turned off to constrain the dependence of certain correlation functions on the untwisted moduli. This allows us to approach the problem of what happens when one tries to deform away from the \LG\ point. In particular, we find that the masses and three-point couplings of the massless $E_{6}$ singlets related to ${\rm H^{1}}(\ET)$ vanish at all points in the quintic \Ka\ moduli space. Putting these results together, and invoking some plausible dynamical assumptions about the corresponding linear \sm s, we show that one can deform these \LG\ theories to arbitrary values of the \Ka\ moduli.