Heterotic de Sitter beyond modular symmetry

Abstract

We study 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. 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 Kähler 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.

Fermion masses, critical behavior and universality

“…[96], it was conjectured that all extrema of V (τ, τ ) are at CP-conserving values of τ , that is either on the boundary of the fundamental domain or on the imaginary τ axis. Only recently, CP-violating minima have also been found [97,98]. They lie in the vicinity of the fixed point τ = ω, at a typical distance |τ − ω| of order 0.01, and require n = 0 and m = 0.…”

“…They lie in the vicinity of the fixed point τ = ω, at a typical distance |τ − ω| of order 0.01, and require n = 0 and m = 0. Both the minima close to τ = i and those near τ = ω correspond to a negative cosmological constant but, depending on the integers (m, n), variants of V (τ, τ ) can exhibit local minima with a positive energy density [98]. Turning on additional moduli and/or fluxes leads to a richer variety of possibilities.…”

CP symmetry and symplectic modular invariance

“…Remarkably, fixed points τ 0 are extrema of a modular invariant energy density [45,46]. Moreover, minima of the energy density close to but distinct from the fixed points have been established in modular invariant theories [47][48][49][50][51]. Cosmological evolution can offer a mechanism for moduli trapping near the points enjoying an enhanced symmetry [52][53][54].…”

A Note on Modular Invariant Species Scale and Potentials

“…[24–30] and it has recently experienced renewed interest, e.g., in refs. [31–33] We will recall some aspects of these models and give support to the idea that the species scale can be identified with their topological free energy. We will also explain how, when choosing to preserve modularity instead of holomorphy of the species scale, additive logarithmic corrections arise in such a way that $$\Lambda _{sp}$$ turns out to be slightly larger than the string scale.…”