Description
Abstract: Heterotic worldsheet instanton contributions to the 4D N=1 superpotential depend on Kahler, complex structure, and bundle moduli of the underlying string compactification. Beasley-Witten and Bertolini-Plesser used sigma model arguments to show that these contributions can exhibit a surprising cancelation among different curves within the same curve class. We will analyze this cancelation from an algebraic point of view for monad or extension bundles over complete intersection Calabi-Yau (CICY) manifolds. We give a purely algebraic way of computing the genus zero, single wrapping, Gromov-Witten invariants for a specific type of curve class, illustrate how to compute the Pfaffians and their moduli dependence up to a constant, and study the aforementioned cancelation for these classes of models. We find connections between the polynomials governing the Pfaffians and the mixed GLSM anomalies, and formulate a necessary condition for a non-vanishing instanton superpotential in terms of an affine Hilbert function. Surprisingly, all models found in a scan over monad bundles on CICYs with Picard number 3 have linear dependent Pfaffian contributions (and hence potential cancelations) within a given curve class, even when the instanton moduli space is non-compact and hence the arguments of Beasley-Witten do not enforce such a vanishing.
