D-brane instantons on non-Spin cycles

TL;DR

The paper demonstrates that non-Spin cycles in type IIB Calabi–Yau orientifolds with $B=0$ naturally support orientifold-invariant D-brane instantons, specifically an invariant rank-2 instanton described by $i_*oldsymbol{ abla}$ on the non-Spin cycle, which can contribute to the superpotential. Using a Spin$^c$ framework via sheaf language, it shows that the instanton has exactly the two universal fermionic zero modes $ heta^{oldsymbol{eta}}$ and no extra neutral or charged zero modes for a chosen D7 flavor-brane configuration, ensuring a non-perturbative superpotential term $W_{ m non-pert}=A_{1- ext{loop}} e^{-S_{ m inst}}$ with $S_{ m inst}$ tied to the central charge $Z(i_*oldsymbol{ abla})$. A small-volume (quiver/orbifold) interpretation identifies the invariant node with an $O(1)$ gauge instanton, reinforcing the non-perturbative dynamics in the invariant sector and linking to D3-brane moduli. The results suggest a robust mechanism for Kähler moduli stabilization and hint at broader generalizations to higher-rank or non-rigid instantons with worldvolume flux, with potential applications in moduli stabilization scenarios.

Abstract

We show that non-Spin cycles in type IIB Calabi-Yau orientifold compactifications with vanishing B field naturally support orientifold-invariant D-brane instantons. These instantons, associated to the holomorphic cotangent bundle of the non-Spin cycle, can lead to non-perturbative corrections to the superpotential.