Systematic classification of fluxes in the 2^6 and 1^9 Landau–Ginzburg orientifolds

Classify all supersymmetric imaginary self-dual three-form flux configurations consistent with the D3-brane tadpole cancellation bound in the type IIB Landau–Ginzburg 2^6 orientifold model (with N_flux ≤ 40), and complete the analogous classification for the 1^9 model (with N_flux ≤ 12), thereby producing an exhaustive dataset of resulting four-dimensional N=1 Minkowski vacua in these backgrounds.

Background

The proceedings focus on non-geometric type IIB compactifications with exact worldsheet descriptions, specifically the 1^9 and 2^6 Landau–Ginzburg orientifold models that are mirrors of rigid Calabi–Yau threefolds and thus have no Kähler moduli. These models offer sharp tests for flux stabilization and swampland conjectures under small tadpole bounds.

The author notes that the 1^9 model is close to a regime where all allowed fluxes with small tadpole are understood, while the 2^6 model is more complex but may admit a broader scan or near-complete classification. Achieving a systematic classification would move from example-based evidence to exhaustive datasets, strengthening conclusions about stabilization efficiency and conjecture tests.