The String Universe: High $T_c$ Superconductor or Quantum Hall Conductor?

TL;DR

This paper proposes that space-time singularities can be modeled by topological gauge theories with supersymmetry, linking quantum Hall effects to cosmological phenomena and black hole decay.

Contribution

It introduces a novel theoretical framework connecting topological gauge theories, supersymmetry, and cosmological processes, emphasizing the role of fermions and renormalization group flow.

Findings

Space-time singularities described by Abelian gauge theories with Chern-Simons terms.

Supersymmetry provides a fixed point with Bogomolny bound saturation.

Fermions' complex nature explains the cosmological arrow of time and black hole decay.

Abstract

Our answer is the latter. Space-time singularities, including the initial one, are described by world-sheet topological Abelian gauge theories with a Chern-Simons term. Their effective $N=2$ supersymmetry provides an initial fixed point where the Bogomolny bound is saturated on the world-sheet, corresponding to an extreme Reissner-Nordstrom solution in space-time. Away from the singularity the gauge theory has world-sheet matter fields, bosons and fermions, associated with the generation of target space-time. Because the fermions are complex (cf the Quantum Hall Effect) rather than real (cf high-$T_c$ superconductors) the energetically-preferred vacuum is not parity or time-reversal invariant, and the associated renormalization group flow explains the cosmological arrow of time, as well as the decay of real or virtual black holes, with a monotonic increase in entropy.