Confining backgrounds and quantum chaos in holography

Abstract

Classical world-sheet string theory has recently been shown to be nonintegrable and chaotic in various confining string theory backgrounds -the AdS soliton background in particular. In this paper we study a minisuperspace quantization of the theory and look at properties of the spectrum like the distribution of level spacing, which are indicative of quantum order or chaos. In the quantum spectrum we find a gradual transition from chaotic (Wigner GOE) to integrable (Poisson) regime as we look at higher energies. This is expected since our system is integrable asymptotically, and at higher energies, the dynamics is entirely dominated by the kinetic terms.

Non-integrability in non-relativistic theories

“…It is natural to think therefore that confining backgrounds have a chaotic quantum spectrum in the sense of the Gaussian orthogonal ensemble (GOE) [23]. The quantum spectrum has also been studied in the AdS soliton background where a smooth transition from the Wigner GOE to the integrable regime was noticed as the energy increased, in agreement with the fact that the system becomes asymptotically AdS at higher energies [24]. In [25] the string solutions were studied in curved Dp-brane backgrounds and non-integrability was found except for special cases.…”

Gravitational collapse, chaos in CFT correlators and the information paradox

“…In the framework of string theory, the KG equation for the scalar field Ψ is itself an approximation for the corresponding vertex operator. This would correspond to a regime analogous to quantum chaos; in some restricted sense similar problems become tractable (see [32,33] for work in the context of confinement). It is expected that in the stringy treatment of the field Ψ the types of questions that can be formulated change considerably.…”

A quantum Rosetta Stone for the information paradox

“…Note that equation (3.2) would correspond to allowing only the center of mass degrees of freedom. The work presented in [18] and [19] kept some degrees of freedom related to the spatial extension of the string and was able to produce a spectrum for holographic hadrons that matches qualitatively those of real hadrons following the Particle Data Table. Towards Chaotic Quantum Field Theory in Curved Spaces -One natural question that the current state of affairs suggests is to reconsider Hawking's calculation [1] in the context of chaotic classical dynamics. Classical solutions play an important role in the Hawking process.…”