Timelike Kasner singularities and Floquet States in 2+1d AdS/CFT

TL;DR

This paper explores how timelike Kasner singularities can be incorporated into a holographic 2+1d CFT model with an oscillating gauge field, revealing Floquet states with unique conductivity properties and analyzing their Kasner exponents.

Contribution

It introduces a novel approach to include Kasner singularities in holographic models, leading to the construction of Floquet states with specific transport phenomena.

Findings

Floquet states exhibit Hall conductivity or kinetic induction.

Kasner exponents are numerically evaluated for various boundary conditions.

Inclusion of Kasner singularities offers new insights into AdS/CFT and cosmology applications.

Abstract

We consider a model of a holographic 2+1d CFT interacting with an oscillating background gauge field. It is solved by an AdS-Vaidya metric describing Ohmic heating of the boundary field theory. However, we also show that if timelike singularities of Kasner type are permitted then a time independent solution that may be interpreted as a Floquet state of the system can be constructed. In this state the system exhibits either Hall conductivity or kinetic induction, and we numerically evaluate the Kasner exponents for a range of boundary conditions. This model may contribute to the ongoing discussion on the validity and meaning of the Kasner metric in the AdS/CFT correspondence and its application in cosmology.