Brane Inflation and Moduli Stabilization on Twisted Tori

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.