Heterotic de Sitter Beyond Modular Symmetry

TL;DR

This paper investigates the existence of de Sitter vacua in heterotic string theory compactifications, proving no-go theorems, identifying conditions for metastable vacua, and exploring stringy effects that could enable de Sitter solutions.

Contribution

It extends previous no-go theorems for de Sitter vacua in heterotic models and identifies potential loopholes and stringy effects that could realize such vacua.

Findings

Proved three de Sitter no-go theorems for certain vacua classes

Found that extrema can occur inside the fundamental domain, challenging previous conjectures

Identified stringy non-perturbative effects that might enable de Sitter vacua

Abstract

We study the vacua of $4d$ heterotic toroidal orbifolds using effective theories consisting of an overall K\"{a}hler modulus, the dilaton, and non-perturbative corrections to both the superpotential and K\"{a}hler 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$(2,\mathbb{Z})$ fundamental domain of the K\"{a}hler 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