Freezing E3-brane instantons with fluxes

TL;DR

This work develops a covariant framework for E3-instantons in IIB with varying axio-dilaton, incorporating SL$(2,\mathbb{Z})$ monodromies and worldvolume fluxes. By mapping E3 zero-modes to twisted cohomologies and connecting to M5-instanton counting in F-theory, it derives an IIB index $\chi_{\rm E3}$ that governs superpotential generation and demonstrates how worldvolume flux can, for example, freeze non-rigid divisors to yield exactly two universal fermionic zero-modes. The authors provide an explicit flux construction in a one-modulus Calabi-Yau to realize a magnetized E3-brane contributing to the superpotential, and they show the lifting mechanism is consistent with the geometric lifting of moduli. A concrete one-modulus example illustrates the practicality and ubiquity of flux-induced rigidification, suggesting many more instanton corrections to the superpotential in realistic IIB compactifications and important implications for moduli stabilization and the string landscape.

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.

Figures (1)

• Figure 1: Schematic description of the relation between E3 and M5 fermionic zero modes. Here $h^k({\rm E3})\equiv h^{0,k}_{\bar{\partial}}(D)$, $h^k_Q({\rm E3})\equiv h^k_Q(D) = \dim H^k(D, {\cal L}^{-1}_Q)$ and $h^{k}({\rm M5})\equiv\dim H^{0,k}_{\bar{\partial}}(\hat{D})$. The zero modes $\lambda^\alpha_{\rm z.m.}$ and $\tilde{\lambda}_{\rm z.m.}^{\dot\alpha}$ correspond to the universal zero modes crucially studied in Bianchi:2007fx, often denoted by $\theta^\alpha$ and $\bar{\tau}^{\dot\alpha}$ respectively, of D-brane instantons in orientifold vacua.