Holographic Thermalization, Stability of Anti–de Sitter Space, and the Fermi-Pasta-Ulam Paradox

Abstract

For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to anti-de Sitter space (AdS) but whose numerical evolution does not result in black hole formation. According to the AdS/conformal field theory (CFT) dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-time-scale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasiperiodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem.

Missing top of the AdS resonance structure

“…It was also observed that half of the naïvely expected channels to transfer energy are actually absent, which leads to extra conserved quantities. This may explain the stable, quasiperiodic solutions which are also often observed during numerical simulations [6,[10][11][12].…”

“…Here we will revisit the proof of those conservation laws and show that they are also valid in the ϕ 4 theory even without spherical symmetry. We first follow the two-time formalism introduced in [10]. Instead of the naïve perturbative expansion in Eq.…”

Unstable horizons and singularity development in holography

“…In the context of holography, early indications supported this for generic far-from-equilibrium, arbitrary low-energy states of strongly coupled conformal gauge theories, even when the dynamical evolution of these states was artificially restricted to symmetric submanifolds of the full phase space of the theory 9 [29,30]. Shortly thereafter it was argued [31][32][33] that in fact symmetric phase space of holographic conformal field theories has islands of stability that never equilibrate. In this study we identified yet another possibility: initial states of holographic strongly coupled gauge theories, well described classically in the gravitational frame, evolve to a singularity in finite time.…”

Weak field collapse in AdS: introducing a charge density

“…A priori, E initial and ∆E are independent. However, in our case, we already demanded E initial ∼ ∆E and thus, using dimensional analysis, we can arrive at 28) where α 1,2 are two constants and A denotes the area of the entangling surface.…”