Universality of Dissipation across Holographic Interfaces

TL;DR

The paper investigates how dissipation and relaxation propagate across a holographic interface in a two-dimensional ICFT by coupling a supersymmetric Janus geometry to a BTZ bath via a double-trace deformation. It introduces the Liouvillian-gap-based observable $c_\text{relax}$, defined as the ratio of the lowest imaginary parts of the quasinormal-mode spectrum with and without the interface, and demonstrates its universality: $c_\text{relax}$ is largely insensitive to coupling details such as the strength $h$, operator dimension $\Delta$, and the coupling position, while being governed primarily by the interface geometry. The numerical analysis reveals that $c_\text{relax}$ tracks equilibrium interface observables, with $c_{\text{eff}}=1/\kappa$ and $c_{LR}=1/\kappa^2$ providing reference scales, and that $c_\text{relax}$ closely matches $c_{\text{eff}}$ across the parameter range. Together, these results support $c_\text{relax}$ as a universal dynamical characteristic of dissipative interface dynamics in 2D holographic ICFTs and motivate exploration of additional holographic setups to test its universality.

Abstract

Motivated by recent results in spin chains we study dissipation and relaxation in a two-dimensional holographic interface conformal field theory (ICFT) in which degrees of freedom on one side of the interface are coupled to an external bath, while the other side remains isolated. In the bulk description this setup is realized by gluing a supersymmetric Janus geometry to a BTZ black hole region, with the coupling implemented through a double-trace deformation. We determine the quasinormal modes in the bulk by solving the double-trace matching conditions of the system and bath. The lowest imaginary part of the modes defines a Liouvillian gap, and following earlier work in spin chains we introduce the dimensionless ratio crelax as a measure of interface-induced suppression of relaxation. Numerically we find that, crelax is independent of coupling details to the bath. It is a strong candidate for a universal interface observable characterizing dissipation and relaxation across the interface.

Figures (3)

• Figure 1: The quasinormal modes of BPS-Janus for $\Delta=1.3$, $\kappa=1$ (blue) and $\kappa=1.5$ (red), at fixed coupling $g\equiv |(2\Delta-2)|h=0.1$. The green line is their ratio $c_\text{relax}$ shown on the right y-axis, signaling its independence of the position of insertion of dissipation.
• Figure 2: The dependence of $c_\text{relax}$ on $h$ and $\Delta$ is within our numerical precision ($10^{-4}$), supporting its universality.
• Figure 3: $c_{\text{relax}}$ (red dots) versus the BPS-Janus deformation parameter $\kappa$. The green line is the energy transmission coefficient $c_{LR}=1/\kappa^2$, and the blue line is the entanglement entropy across the interface $c_\text{eff}=1/\kappa$, which almost exactly fits $c_\text{relax}$ up to our numerical precision.