Stringy Instantons in IIB Brane Systems
Shamit Kachru, Dusan Simic
TL;DR
The paper addresses non-perturbative corrections to the 4d superpotential from stringy D-brane instantons in Type IIB Calabi-Yau compactifications. For rigid instantons, it shows these corrections can be computed from the tree-level superpotential of an auxiliary gauge theory using topological B-model methods governed by an $A_{\infty}$-structure. The key result is a simple holomorphic formula, $\Delta W \propto e^{-t}\det M(\Phi) M(\Phi)_{ij}$, with coefficients determined by derivatives of the auxiliary theory's $\bf W$ and by determinants of massive modes; the framework extends to wrapping a massive $U(1)$ node, which lifts extra zero modes. The paper also discusses non-rigid instantons, where holomorphic corrections involve correlators of adjoint matter and remain expressible in terms of the auxiliary theory, suggesting a general path to computing non-perturbative corrections in broad Calabi–Yau brane setups. Overall, the work provides a practical route to evaluate stringy instanton effects across toric and more general CY geometries by tying worldsheet CFT data to topological-string computations via an auxiliary gauge theory.
Abstract
In this note, we study D-brane instantons which intersect N=1 supersymmetric configurations of space-filling D-branes in general Calabi-Yau compactifications of type IIB string theory. Our focus is on rigid ``stringy instantons'' -- those which cannot be interpreted as Yang-Mills instantons in a non-Abelian gauge group on any stack of space-filling D-branes. We show that their contributions to the space-time superpotential can be determined by a topological B-model computation of the tree-level superpotential for a related auxiliary brane system. This computation is very tractable, as it is governed by an A-infinity structure. We summarize the stringy instanton contribution to the space-time superpotential in a simple formula.