Relate holographic and lattice relaxation coefficients

Determine the precise relation between the holographic ultraviolet quantity $c_{\rm UV}$ and the lattice open-system relaxation coefficients $c^{\rm global}_{\rm relax}$ and $c_{\rm relax}$ for dissipation across conformal interfaces.

Background

The paper compares two approaches to universal dissipation suppression across conformal interfaces. In lattice open quantum critical systems, $c^{\rm global}_{\rm relax}$ is defined from the Liouvillian gap, while the paper introduces the mode-resolved coefficient $c_{\rm relax}$ to avoid ambiguities caused by mode switching. Separately, a holographic study defines a projected ultraviolet quantity $c_{\rm UV}$ from the damping of bulk modes in an interface CFT coupled to a thermal bath.

Both approaches exhibit universal behavior related to interface transmission, but the paper does not establish whether the holographic quantity is equivalent to either lattice relaxation coefficient, nor how the quantities are mathematically related. Resolving this relation would connect strongly coupled holographic dissipation to solvable lattice models of open quantum critical dynamics.