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We describe a method for finding flux vacua of type IIB string theory in which the Gukov-Vafa-Witten superpotential is exponentially small. We present an example with W₀210^-8 on an orientifold of a Calabi-Yau hypersurface with (h^1, 1, h^2, 1) = (2, 272), at large complex structure and weak string coupling.
Demirtaş et al. (Thu,) studied this question.