Abstract
We study the quasinormal modes and non-linear dynamics of a simplified model of semi-holography, which consistently integrates mutually interacting perturbative and strongly coupled holographic degrees of freedom such that the full system has a total conserved energy. We show that the thermalization of the full system can be parametrically slow when the mutual coupling is weak. For typical homogeneous initial states, we find that initially energy is transferred from the black brane to the perturbative sector, later giving way to complete transfer of energy to the black brane at a slow and constant rate, while the entropy grows monotonically for all time. Larger mutual coupling between the two sectors leads to larger extraction of energy from the black brane by the boundary perturbative system, but also quicker irreversible transfer of energy back to the black brane. The quasinormal modes replicate features of a dissipative system with a softly broken symmetry including the so-called k-gap. Furthermore, when the mutual coupling is below a critical value, there exists a hybrid zero mode with finite momentum which becomes unstable at higher values of momentum, indicating a Gregory-Laflamme type instability. This could imply turbulent equipartitioning of energy between the boundary and the holographic degrees of freedom in the presence of inhomogeneities.
Highlights
Considers both subsectors at any scale, it is expected that the perturbative sector should dominate the ultraviolet behavior while the infrared behavior will be governed by the dynamics of the dynamical black hole horizon of the holographic sector
We study the quasinormal modes and non-linear dynamics of a simplified model of semi-holography, which consistently integrates mutually interacting perturbative and strongly coupled holographic degrees of freedom such that the full system has a total conserved energy
For typical homogeneous initial states, we find that initially energy is transferred from the black brane to the perturbative sector, later giving way to complete transfer of energy to the black brane at a slow and constant rate, while the entropy grows monotonically for all time
Summary
The construction of the semi-holographic framework is based on the following principles: 1. The non-perturbative part of the dynamics can be described by a strongly coupled large N holographic theory. The non-perturbative part of the dynamics can be described by a strongly coupled large N holographic theory. The marginal and relevant couplings, and the effective background metric of each sector are promoted to ultralocal algebraic functions of the operators of the other sector in such a way that the full system has a local and conserved energy-momentum tensor in the physical background metric [4, 5]. This coupling scheme is called democratic coupling [4]. Numerous non-trivial examples explicitly demonstrate that the iterative procedure converges [7, 8] with the present article serving as another such demonstration
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