Freezing E3-brane instantons with fluxes

E3‐instantons that generate non‐perturbative superpotentials in IIB N = 1 compactifications have a much more frequent occurrence 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 modes 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 E3 worldvolume fluxes can be explicitly constructed in a one‐modulus compactification, such that the instanton has exactly two fermonic zero‐modes. This construction is readily applicable to numerous scenarios.