A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry

TL;DR

This paper develops a holographic model of magnetohydrodynamics that reveals new symmetry principles and matrix-valued resistivity, with specific results on viscosities and conformality conditions.

Contribution

It introduces a holographic magnetohydrodynamics model with SO(3) symmetry and analyzes resistivity and viscosity properties, highlighting novel features and conformality aspects.

Findings

Resistivity becomes matrix-valued with antisymmetric parts showing UV-dependent features.

Bulk viscosity is proportional to shear viscosity, indicating conformality.

The model exhibits an SO(3) symmetry that simplifies the description of magnetohydrodynamics.

Abstract

We study magnetohydrodynamics using holography. The gravity model is closely related to the STU supergravity in five dimensions and admits an analytical black brane solution carrying the conserved charge dual to the magnetic 1-form symmetry of the magnetohydrodynamic system. The black brane solution features a fortuitous SO(3) symmetry, providing a new symmetry principle for describing the magnetohydrodynamics. Since the bulk theory contains multiple 2-form gauge fields, the resistivity becomes matrix-valued. We find that the antisymmetric part of the resistivity matrix exhibits novel features depending on the UV cut-off of the theory. We also compute the shear and bulk viscosities and find that the bulk viscosity is proportional to the shear viscosity. Remarkably, the proportionality constant is exactly what is required for conformality, despite the zeroth-order energy-momentum tensor not being trace-free.