Nonequilibrium dynamics of the O(N ) model on dS3 and AdS crunches

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

Quasinormal modes and holographic correlators in a crunching AdS geometry

“…In two related works [26,38] in the case of three specific microscopic models with d = 3 and 4 we find that the exponent γ = 1/d. In this article we will focus our attention on the AdS 4 deformation (discussed in [26]) which happens to be analytically tractable.…”

“…The potential has certain generic features and some specific ones which have been found to hold across different examples [38]. On general grounds V (z) decays exponentially whilst approaching the bulk horizon, z → ∞ and diverges as V (z) ∼ z −2 near z = 0, the conformal boundary.…”

“…When the exponent in (2.5) satisfies γ < 2/(d + 1), the potential term is driven to negative infinity. This is the case for examples studied in [26,38]. For the AdS 4 deformation that we focus on in this paper [26], γ = 1/3 and the Schrödinger potential diverges as V (z) ∼ − 1 4 (z − z c ) −2 at the crunch singularity.…”

“…This brings us to a slightly puzzling feature not shared by relevant deformations yielding crunches in higher dimensions. In [38], where we analyze mass deformations of N = 4 SYM on S 4 , dialling the deformation beyond a critical value forces the theory into a "gapped" Euclidean phase which results, upon analytic continuation, in a Lorentzian geometry without a crunch. This does not appear to be the case for the relevant deformation of the 3d theory we have analysed in this paper and it would be interesting to understand the origin of this difference.…”

RG flows on $S^d$ and Hamiltonian truncation

“…In the case of de Sitter space, the quantization in question was recently used in Ref. [55], which studied the large-N limit of the O(N ) fixed point on dS 3 using gap equations.…”