On (de Sitter) Vacua in Heterotic String Theory

Abstract: Heterotic toroidal orbifolds are a powerful framework for testing our understanding of string vacua. We review recent advances in heterotic model building, from constructing new vacua to proving novel de Sitter no-go theorems. We also illustrate a potential loophole that could pave the way for the realisation of de Sitter vacua within heterotic string theories. This involves the introduction of non-perturbative, stringy, dilaton-dependent corrections to the K\"ahler potential. We discuss how recently found non-BPS heterotic instantons might provide the necessary corrections.