DC conductance and memory in 3D gravity

TL;DR

This paper explores the transport properties and DC conductance in a 2D dual of AdS3 gravity, revealing a gravitational memory effect linked to boundary conditions and anisotropic chiral bosons.

Contribution

It introduces a novel boundary condition framework in AdS3 gravity that models anisotropic scaling and connects gravitational memory to linear response in the dual theory.

Findings

DC conductance depends on the theory level and dynamical exponents

Boundary conditions induce a gravitational memory effect

The process results in a permanent spacetime deformation

Abstract

Transport properties are investigated in the two-dimensional dual dynamics of AdS$_{3}$ gravity. By providing boundary conditions that deform the ADM lapse and shift functions, we construct a lower dimensional model comprising two copies of chiral boson excitations with anisotropic scaling symmetry. Using bosonization, an electric current is identified. By means of the Kubo formula, we find a DC conductance depending on the level of the theory and the dynamical exponents. The bulk realization of the linear response is related to a type of gravitational memory emerging in the context of near-horizon boundary conditions. The process is adiabatic and represents a permanent spacetime deformation parametrized by anisotropic chiral bosons through a large gauge transformation.