Freezing E3-brane instantons with fluxes

TL;DR

This paper investigates how fluxes on E3-branes in type IIB string theory can lift certain zero-modes, ensuring the generation of non-perturbative superpotentials, and provides explicit constructions for such flux configurations.

Contribution

It offers a comprehensive analysis of flux effects on E3-brane zero-modes, incorporating SL(2,Z) monodromies, and presents explicit flux constructions in simple compactifications.

Findings

Fluxes lift geometric moduli and fermionic zero-modes of E3-branes.

Derived a generalized index for superpotential generation in IIB.

Constructed explicit flux configurations with exactly two fermionic zero-modes.

Abstract

E3-instantons that generate non-perturbative superpotentials in IIB N=1 compactifications are more frequent than currently believed. Worldvolume fluxes will typically lift the E3-brane geometric moduli and their fermionic superpartners, leaving only the two required universal fermionic zero-modes. We consistently incorporate SL(2, Z) monodromies and world-volume fluxes in the effective theory of the E3-brane fermions and study the resulting zero-mode spectrum, highlighting the relation between F-theory and perturbative IIB results. This leads us to a IIB derivation of the index for generation of superpotential terms, which reproduces and generalizes available results. Furthermore, we show how worldvolume fluxes can be explicitly constructed in a one-modulus compactification, such that an E3-instanton has exactly two fermonic zero-modes. This construction is readily applicable to numerous scenarios.