Branes and instantons at angles and the F-theory lift of O(1) instantons

TL;DR

The paper analyzes D-brane instantons that intersect at angles, showing that generic configurations do not contribute to the superpotential because extra fermionic zero modes remain unsaturated. It combines a microscopic CFT treatment of the instanton spectrum with effective field theory arguments to explain when zero modes can be lifted, highlighting the special roles of homologically aligned (gauge) and O(1) instantons. It also discusses how certain instantons can evade these obstructions via Coulomb/Higgs-type dynamics and how O(1) instantons lift in F-theory, where orientifold-induced monodromies project out the troublesome modes. The results illuminate constraints on nonperturbative superpotential generation and clarify how F-theory lifts map to the weakly coupled brane configurations.

Abstract

We discuss the physics of D-branes and D-brane instantons intersecting at angles, focusing on the (non)generation of a superpotential in the worldvolume theory of the branes. This is a short review of the results in arXiv:0905.1694, where we further emphasize both the macroscopic and microscopic structure of the manifestly supersymmetric instanton action. We also comment on the lift of O(1) instantons to F-theory.

Figures (1)

• Figure 1: Schematic representation of the Euclidean D3-brane worldvolume theory after the orientifold splits, close to the orientifold locus. The two dots denote the location of the $B$ and $C$ defects. We have omitted the directions common to the $O7^-$ and the Euclidean D3. The dotted green line denotes the contour along which we compute the monodromy. It factorizes into the two smaller dashed contours around each elementary degeneration.