Nonequilibrium dynamics of the O(N) model on dS_3 and AdS crunches

TL;DR

This paper investigates the nonperturbative quantum evolution of the large-N O(N) model on a two-sphere with diverging couplings, revealing regular behavior and fixed point approach despite classical singularities, with implications for AdS crunch resolutions.

Contribution

It demonstrates that quantum effects can regularize classical singularities in the O(N) model on curved spacetime and explores the model's behavior near the Wilson-Fisher fixed point.

Findings

Quantum evolution remains finite at classical singularities.

Time evolution approaches the Wilson-Fisher fixed point.

Quantum backreaction influences the mass dynamics.

Abstract

We study the nonperturbative quantum evolution of the interacting O(N) vector model at large-N, formulated on a spatial two-sphere, with time dependent couplings which diverge at finite time. This model - the so-called "E-frame" theory, is related via a conformal transformation to the interacting O(N) model in three dimensional global de Sitter spacetime with time independent couplings. We show that with a purely quartic, relevant deformation the quantum evolution of the E-frame model is regular even when the classical theory is rendered singular at the end of time by the diverging coupling. Time evolution drives the E-frame theory to the large-N Wilson-Fisher fixed point when the classical coupling diverges. We study the quantum evolution numerically for a variety of initial conditions and demonstrate the finiteness of the energy at the classical "end of time". With an additional (time dependent) mass deformation, quantum backreaction lowers the mass, with a putative smooth time evolution only possible in the limit of infinite quartic coupling. We discuss the relevance of these results for the resolution of crunch singularities in AdS geometries dual to E-frame theories with a classical gravity dual.