Moduli stabilization in asymptotic flux compactifications

A bstract We present a novel strategy to systematically study complex-structure moduli stabilization in Type IIB and F-theory flux compactifications. In particular, we determine vacua any asymptotic regime of the space by exploiting powerful tools Hodge theory. leading approximation dependence vacuum conditions are shown be polynomial with given sl(2)-weights fluxes. This simple algebraic can extracted regime, even though nearly all regimes essential exponential corrections have for consistency. give pedagogical introduction sl(2)-approximation as well detailed step-by-step procedure constructing corresponding star operator. To exemplify construction, analysis several Calabi-Yau three- fourfold examples. For these examples illustrate that match obtained rather well, behaviour tadpole contribution Finally, discuss structure loci their relations swampland conjectures. comment on realization so-called linear scenario view conjecture.