Time-dependent stabilization in AdS/CFT

TL;DR

This paper investigates how time-dependent Hamiltonians in quantum field theories and their gravity duals can be dynamically stabilized, preventing singularities like big crunches through high-frequency oscillations and specific compactification schemes.

Contribution

It introduces a novel approach to stabilizing unbounded potentials in AdS/CFT using time-dependent deformations and number theory techniques to avoid resonances.

Findings

High-frequency oscillations stabilize the system.

Dynamical stabilization prevents big crunch singularities.

Black hole horizons form to screen singularities.

Abstract

We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We first study a free field theory on a torus with a time-dependent mass term, finding that the stability regions are described in terms of the phase diagram of the Mathieu equation. Using number theory we have found a compactification scheme such as to avoid resonances for all momentum modes in the theory. We further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities; we study when such singularities can be cured by dynamical stabilization. We numerically solve the Einstein-scalar equations of motion in the case of a time-dependent doubletrace deformation and find that for sufficiently high frequencies the theory is dynamically stabilized and big crunches get screened by black hole horizons.