Holographic chiral shear waves from anomaly

TL;DR

The paper examines how the 4D U(1)^3 anomaly affects hydrodynamic-like excitations in a strongly coupled N=4 SYM plasma by holographically analyzing fluctuations around a charged AdS black-brane with a 5D Chern-Simons term. A helicity-based decomposition reveals that only the helicity ±1 transverse shear modes acquire parity-odd contributions from the CS term, yielding chiral dispersion relations. Using a long-wavelength expansion and an integral solution approach, the authors derive the dispersion relations, showing a standard diffusive term plus a helicity-dependent cubic correction driven by the anomaly. These results connect holographic quasi-normal mode analysis with anomalous transport in strongly coupled plasmas and provide a concrete strong-coupling realization of chiral shear waves.

Abstract

We study dispersion relations of hydrodynamic waves of hot N=4 SYM plasma at strong coupling with a finite U(1) R-charge chemical potential via holography. We first provide complete equations of motion of linearized fluctuations out of a charged AdS black-hole background according to their helicity, and observe that helicity +1 and -1 transverse shear modes receive a new parity-odd contribution from the 5D Chern-Simons term, which is dual to 4D U(1)^3 anomaly. We present a systematic solution of the helicity +1,-1 wave equations in long wave-length expansion, and obtain the corresponding dispersion relations. The results depend on the sign of helicity, which may be called chiral shear waves.