Moduli stabilization with F-term uplifting in heterotic string theory

In this work, we examine the role of F-term uplifting in stabilizing moduli within the framework of heterotic string theory. In turns out that the uplifting sector plays an important role in stabilizing both the dilaton and the volume modulus. To fix the volume modulus at a self-dual point of modular invariant potential, the modular weight of uplifting field is required to satisfy certain conditions. Generalizing to the case with an anomalous U(1) gauge symmetry, we also study its implications for supersymmetry breaking. It is found that the U(1) sector gives contributions to soft terms which are generically comparable to the dilaton mediated contributions.