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