Dualities versus Singularities

TL;DR

The paper addresses cosmology in M-theory compactified on tori and demonstrates that a subgroup of the U-duality group imposes a Lorentzian structure on the moduli space, separating regions that can be described by weakly coupled 11D SUGRA or Type II theories from those that cannot. It shows that cosmological Kasner singularities can be resolved by duality transformations through the appearance of new light states, while regions outside the safe domain violate holography. A natural arrow of time emerges: the future direction is the approach toward the safe moduli-space domain, with all Kasner solutions interpolating between a holographically pathological past and a safe future. While developed for maximal SUSY toroidal compactifications, the framework is argued to generalize conceptually to less SUSY moduli spaces, suggesting a universal M-theoretic underpinning for early-universe cosmology. Together, these results connect minisuperspace quantum cosmology with exact M-theory dualities, offering a principled way to discuss singularities, holography, and time's arrow in a nonperturbative setting.

Abstract

We show that a subgroup of the modular group of M-theory compactified on a ten torus, implies the Lorentzian structure of the moduli space, that is usually associated with naive discussions of quantum cosmology based on the low energy Einstein action. This structure implies a natural division of the asymptotic domains of the moduli space into regions which can/cannot be mapped to Type II string theory or 11D Supergravity (SUGRA) with large radii. We call these the safe and unsafe domains. The safe domain is the interior of the future light cone in the moduli space while the unsafe domain contains the spacelike region and the past light cone. Within the safe domain, apparent cosmological singularities can be resolved by duality transformations and we briefly provide a physical picture of how this occurs. The unsafe domains represent true singularities where all field theoretic description of the physics breaks down. They violate the holographic principle. We argue that this structure provides a natural arrow of time for cosmology. All of the Kasner solutions, of the compactified SUGRA theory interpolate between the past and future light cones of the moduli space. We describe tentative generalizations of this analysis to moduli spaces with less SUSY.