Brane Inflation and Moduli Stabilization on Twisted Tori

TL;DR

This work examines brane-induced inflation and moduli stabilization within massive Type IIA supergravity on twisted tori, focusing on monodromy-driven inflaton potentials and the feasibility of achieving de Sitter vacua with small cosmological constants. By performing Scherk–Schwarz reductions and analyzing the 4D effective potential U(g,μ), the authors classify possible power-law inflaton potentials and derive a no-go result: in broad twisted-torus setups where all localized sources wrap the base circle, Δ = 4ac/b^2 cannot be stabilized to yield parametrically small CC. They further study discrete Wilson lines, showing gauge invariance constrains their contributions to tilde F_4 fluxes and that fractional shifts can occur under certain global conditions, especially on twisted tori. The paper culminates with a detailed O6-twisted-torus example, computing cohomology, fluxes, tadpoles, KK5 contributions, and the full effective potential, which again exhibits a run-away behavior precluding small CC vacua in this class. Overall, the work delineates both the potential inflationary mechanisms on twisted tori and the stringent challenges to moduli stabilization and de Sitter realizations in these backgrounds, while outlining pathways that might evade the no-go in more general constructions.

Abstract

We consider supergravity compactifications on 6-dimensional twisted tori, which are 5-torus fibrations of the circle. The motion of branes on such manifolds can lead to power-law potentials at low energy, that may be useful for inflation. We classify the possible low energy potentials one can obtain by wrapping branes on different cycles of the fibre. Turning to the problem of moduli stabilization in such models, we prove a no-go result for solutions with parametrically small cosmological constant, under certain assumptions for the orientifolds and D-branes. We also consider the role of discrete Wilson lines in moduli stabilization on general closed manifolds, and show that gauge invariance restricts their contributions to the effective potential. We derive the allowed discrete Wilson lines in massive Type IIA supergravity on twisted tori. We conclude with a detailed example, computing the effective potentials in a class of models involving a twisted torus and an orientifold 6-plane.