Holographic subdiffusion

TL;DR

This paper explores charge transport in strongly coupled quantum systems with dipole conservation using holography, revealing subdiffusive behavior characterized by a fourth-order diffusion equation.

Contribution

It introduces a holographic model with a mixed-rank tensor to describe boundary multipole symmetries and demonstrates subdiffusive charge relaxation at finite temperature.

Findings

Charge relaxes via a fourth-order subdiffusion equation

Holographic model encodes multipole symmetry through a mixed-rank tensor

Consistent with recent field-theoretic frameworks

Abstract

We initiate a study of finite temperature transport in gapless and strongly coupled quantum theories with charge and dipole conservation using gauge-gravity duality. In a model with non-dynamical gravity, the bulk fields of our model include a suitable mixed-rank tensor which encodes the boundary multipole symmetry. We describe how such a theory can arise at low energies in a theory with a covariant bulk action. Studying response functions at zero density, we find that charge relaxes via a fourth-order subdiffusion equation, consistent with a recently-developed field-theoretic framework.