The Structure of the Flux Landscape

Identifying flux vacua in string theory with stabilized complex structure moduli presents a significant challenge, necessitating the minimization of a scalar potential complicated by infinitely many exponential corrections. In order to obtain exact results we connect three central topics: transcendentality or algebraicity of coupling functions, emergent symmetries, and the distribution of vacua. We demonstrate these ideas on an explicit example where we determine the landscape of exact flux vacua with a vanishing superpotential. We examine the implications of the tadpole bound, which intriguingly confines flux vacua to real values of the moduli, providing a potential avenue for addressing the strong CP problem.