Residues and world-sheet instantons

Abstract

We reconsider the question of which Calabi-Yau compactifications of the heterotic string are stable under world-sheet instanton corrections to the effective space-time superpotential. For instance, compactifications described by (0, 2) linear sigma models are believed to be stable, suggesting a remarkable cancellation among the instanton effects in these theories. Here, we show that this cancellation follows directly from a residue theorem, whose proof relies only upon the right-moving world-sheet supersymmetries and suitable compactness properties of the (0, 2) linear sigma model. Our residue theorem also extends to a new class of "half-linear" sigma models. Using these half-linear models, we show that heterotic compactifications on the quintic hypersurface in CP 4 for which the gauge bundle pulls back from a bundle on CP 4 are stable. Finally, we apply similar ideas to compute the superpotential contributions from families of membrane instantons in M-theory compactifications on manifolds of G 2 holonomy.

Summing the instantons in half-twisted linear sigma models

“…We find it convenient to adopt the following splitting of the matter fields: we treat separately the fields in the Φ 0 , Γ 0 multiplets and split up the n multiplets according to the degrees d i : 6) where…”

Notes on Certain (0,2) Correlation Functions

“…The first of these properties plays a different 3 and equally important role. We shall see that it is required to make sense of product structures (at both the classical and quantum levels), as well as for the additive structure of the heterotic chiral ring to be well-behaved.…”

“…For example, considerations of (2, 2) sigma models on supermanifolds [7] lead one to study holomorphic vector bundles on Calabi-Yau manifolds, and their extensions over moduli spaces of rational curves. Some related work in heterotic compactifications is [3,8,9,10], where correlation functions of gauge singlets were studied (and shown to vanish). In this paper, we are concerned with heterotic correlation functions between vertex operators for charged states -no gauge singlets appear in our correlation functions, and so the vanishing results of [3,8,9,10] are not relevant.…”

Rational curves and (0, 2)-deformations

“…It may be that each rational curve gives a nonzero contribution to one-point functions, but these contributions magically cancel when all the rational curves are added up. Such a miracle indeed happens for the quintic threefold [8] as was explained further in [9]. The generic quintic has 2875 lines and over each of these lines a generic deformation of T will split trivially.…”

“…More precisely, the analysis of [9] suggests that anything that can be written as a gauged linear σ-model evades instanton effects.…”