On the Search for Low <i>W</i> ₀

The magnitude of the vacuum expectation value Gukov-Vafa-Witten superpotential | W 0 $|W_0|$ plays a central role in phenomenology type IIB flux compactifications. Recent analytical constructions have shown that perturbatively flat vacua can be used to obtain very low values . We present systematic algorithms carry out exhaustive numerical searches for such vacua. also analyse them statistical context, as part entire ensemble at Our preliminary analysis indicates these are statistically sparse whole set calculated by Denef and Douglas. Two-moduli examples illustrate more general findings specific settings. find simple (two moduli) cases good existence proofs but they do not feature large tuning freedom phenomenological applications.