Chern-Simons invariants and heterotic superpotentials

Abstract

The superpotential in four-dimensional heterotic effective theories contains terms arising from holomorphic Chern-Simons invariants associated to the gauge and tangent bundles of the compactification geometry. These effects are crucial for a number of key features of the theory, including vacuum stability and moduli stabilization. Despite their importance, few tools exist in the literature to compute such effects in a given heterotic vacuum. In this work we present new techniques to explicitly determine holomorphic Chern-Simons invariants in heterotic string compactifications. The key technical ingredient in our computations are real bundle morphisms between the gauge and tangent bundles. We find that there are large classes of examples, beyond the standard embedding, where the Chern-Simons superpotential vanishes. We also provide explicit examples for non-flat bundles where it is non-vanishing and non-integer quantized, generalizing previous results for Wilson lines.

String Cosmology: from the Early Universe to Today

“…[312] for the computation of Chern-Simons invariants from Wilson line backgrounds, and Ref. [313] for the same from non-standard embeddings). Vector bundle and Kähler moduli could also be stabilised into a supersymmetric AdS solution once threshold corrections are taken into account.…”

Heterotic complex structure moduli stabilization for elliptically fibered Calabi-Yau manifolds

“…We will take the extension class C i + = 0 not far from the zero in H 1 (X, L 2 ) and keep C j − = 0 in the following. The nontrivial F-term comes from the Gukov-Vafa-Witten superpotential [48,49]. For bundle considered in (2.7), one can show that superpotential from the contribution of bundle moduli is [13] W…”

Eigenvalues and eigenforms on Calabi-Yau threefolds

“…There are now a number of approaches for computing approximate metrics on Kähler manifolds, utilising balanced metrics [46,47], so-called optimal metrics [48], positionspace methods [49], and symplectic coordinates [50]. These have been used to calculate numerical Calabi-Yau metrics [51,52], hermitian Yang-Mills connections [53][54][55], Chern-Simons invariants [56], curvature expansions [57], and moduli space metrics [58]. Most importantly for us, numerical Calabi-Yau metrics have also been used to compute the spectrum of the scalar Laplace operator [1,59].…”