Miracle at the Gepner Point

Abstract

A four-point function of $E_6$ singlets, of interest in elucidating the moduli space of (0,2) deformations of the quintic string vacuum, is computed using analytic and numerical methods. The conformal field theory amplitude satisfies the requisite selection rules and monodromy conditions, but the integrated string amplitude vanishes. Together with selection rules coming from the spacetime R-symmetry \dksecond, this demonstrates the flatness of the gauge-singlet spacetime superpotential through fourth order. Relevance to the more general program of determining the (0,2) moduli space and superpotential is discussed.