D3 instantons in Calabi-Yau orientifolds with(out) fluxes

TL;DR

This paper analyzes D3 instantons in Calabi-Yau orientifolds, focusing on conditions for nonzero superpotentials with and without fluxes, and explores their zero mode structures and implications for string compactifications.

Contribution

It provides a detailed study of D3 instanton effects, zero mode structures, and flux influence, including explicit examples and connections to D5 instantons in Type I theory.

Findings

Fluxes alter the conditions for nonzero superpotentials.

Explicit example in $K3 imes T^2/Z_2$ demonstrates flux effects.

Multi-instanton calculus reduces to field theory in special configurations.

Abstract

We investigate the instanton effect due to D3 branes wrapping a four-cycle in a Calabi-Yau orientifold with D7 branes. We study the condition for the nonzero superpotentials from the D3 instantons. For that matter we work out the zero mode structures of D3 branes wrapping a four-cycle both in the presence of the fluxes and in the absence of the fluxes. In the presence of the fluxes, the condition for the nonzero superpotential could be different from that without the fluxes. We explicitly work out a simple example of the orientifold of $K3 \times T^2/Z_2$ with a suitable flux to show such behavior. The effects of D3-D7 sectors are interesting and give further constraints for the nonzero superpotential. In a special configuration where D3 branes and D7 branes wrap the same four-cycle, multi-instanton calculus of D3 branes could be reduced to that of a suitable field theory. The structure of D5 instantons in Type I theory is briefly discussed.