Heterotic de Sitter beyond modular symmetry

We study the vacua of 4d heterotic toroidal orbifolds using effective theories consisting of an overall Kahler modulus, the dilaton, and non-perturbative corrections to both the superpotential and Kahler potential that respect modular invariance. We prove three de Sitter no-go theorems for several classes of vacua and thereby substantiate and extend previous conjectures. Additionally, we provide evidence that extrema of the scalar potential can occur inside the PSL(2, Z) fundamental domain of the Kahler modulus, in contradiction of a separate conjecture. We also illustrate a loophole in the no-go theorems and determine criteria that allow for metastable de Sitter vacua. Finally, we identify inherently stringy non-perturbative effects in the dilaton sector that could exploit this loophole and potentially realize de Sitter vacua.