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.
Highlights
Been motivated by the hope that at least some of the general lessons learned in this decadespanning and extensive effort will carry over to more realistic situations where all of the moduli are stabilized
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
We begin by formulating the holomorphic Chern-Simons invariant, the object which will provide us with a well-defined version of the Chern-Simons term (1.4) which appears in the heterotic superpotential
Summary
The reader may well be used to defining Chern-Simons invariants in the form discussed in the introduction. In many physical applications such a definition suffices. In the case of heterotic compactifications, the non-trivial topological structure of the compactification means that more care is required. In what follows we will compare the definitions of such invariants as they appear in the physics and mathematics literature, and we will describe why caution is required
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