Dualities versus Singularities

TL;DR

This paper explores how duality symmetries in M-theory compactified on a ten-torus shape the structure of the moduli space, distinguishing regions where cosmological singularities can be resolved from those where they are genuine, thus providing insights into the nature of time and singularities in quantum cosmology.

Contribution

It demonstrates the role of modular group subgroups in defining the Lorentzian structure of the moduli space and introduces the concepts of safe and unsafe domains related to singularities and dualities.

Findings

Safe domain allows resolution of apparent singularities via dualities

Unsafe domain contains true singularities where physics breaks down

Moduli space structure suggests a natural arrow of time in cosmology

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.