Beyond quantum chaos in emergent dual holography

Abstract

Black hole is well known to be a fast scrambler, responsible for physics of quantum chaos in dual holography. Recently, the Euclidean worm hole has been proposed to play a central role in the chaotic behavior of the spectral form factor. Furthermore, this phenomena was reinterpreted based on an effective field theory approach for quantum chaos. Since the graded nonlinear $\sigma-$model approach can describe not only the Wigner-Dyson level statistics but also its Poisson distribution, it is natural to ask whether the dual holography can touch the Poisson regime beyond the quantum chaos. In this study, we investigate disordered strongly coupled conformal field theories in the large central-charge limit. An idea is to consider a quenched average for metric fluctuations and to take into account the renormalization group flow of the metric-tensor distribution function from the UV to the IR boundary. Here, renormalization effects at a given disorder configuration are described by the conventional dual holography. We uncover that the renormalized distribution function shows a power-law behavior universally, interpreted as an infinite randomness fixed point.