Heterotic flux vacua with a small superpotential

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Abstract
A bstract: We study heterotic Calabi-Yau compactifications with NSNS three-form flux in view of moduli stabilisation and investigate whether the value | W 0 | of the flux superpotential evaluated at supersymmetric minima can be small. Unlike in type IIB string theory, heterotic compactifications lack a no-scale structure, so that a non-vanishing flux superpotential generically induces a tree-level scalar potential for all moduli. Controlled moduli stabilisation therefore requires the flux superpotential to be sufficiently small in order to compete with non-perturbative effects. Working within a four-dimensional effective field theory and exploiting the special geometry of Calabi-Yau complex structure moduli spaces, we analyse the complex structure F-term equations and derive two no-go theorems: (1) supersymmetric vacua with vanishing | W 0 |, which would lead to a vanishing tree-level scalar potential as in type IIB, occur only at singular loci in moduli space, and (2) no supersymmetric vacua with small | W 0 | exist in the large complex structure limit. Motivated by these results, we analyse explicit models away from the large complex structure regime using exact period expressions and identify one- and two-parameter examples in which suitable flux choices allow for values of | W 0 | of order unity, with some one-parameter models admitting values moderately below unity. Our findings show that small heterotic flux superpotentials are highly constrained, with the values of | W 0 | found in the examples studied being only marginally compatible with moduli stabilisation.

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