Chiral Anomalous Magnetohydrodynamics in action: effective field theory and holography

TL;DR

This paper develops a holographic model for Chiral Anomalous Magnetohydrodynamics (CAMHD), validating it against effective field theory and enabling exploration of complex phenomena like chiral waves and instabilities in chiral fluids.

Contribution

It constructs a holographic model with dynamical electromagnetic fields and axial anomaly, extending the effective field theory of CAMHD to finite axial backgrounds and validating it via Schwinger-Keldysh analysis.

Findings

Holographic model matches the Landry-Liu SK effective theory.

Model generalizes CAMHD to finite axial background fields.

Enables study of chiral magnetic waves and nonlinear instabilities.

Abstract

Chiral Anomalous Magnetohydrodynamics (CAMHD) provides a low-energy effective framework for describing chiral fluids in the presence of dynamical electromagnetic fields and axial anomaly. This theory finds applications across diverse physical systems, including heavy-ion collisions, the early universe, and Weyl/Dirac semimetals. Along with Schwinger-Keldysh (SK) effective theories, holographic models serve as a complementary tool to provide a systematic formulation of CAMHD that goes beyond the weak coupling regime. In this work, we explore holographic models with $U(1)_A \times U(1)$ symmetry, where the electromagnetic $U(1)$ field is rendered dynamical through mixed boundary conditions applied to the bulk gauge field and the axial anomaly is introduced via a Chern-Simons bulk term. Through a detailed holographic SK analysis, we demonstrate that the low-energy effective action derived from this model aligns precisely with the SK field theory proposed by Landry and Liu and, in fact, it generalizes it to scenarios with finite background axial field. This alignment not only validates the holographic model but also paves the way for its use in exploring unresolved aspects of CAMHD, such as the recently proposed chiral magnetic electric separation wave and nonlinear chiral instabilities.