An Effective Theory Of Anomalous Momentum Diffusion From Holography

TL;DR

This paper develops a holographic effective theory for anomalous momentum diffusion in a 5D Maxwell-Chern-Simons model, revealing how quantum anomalies influence boundary currents and their dynamics.

Contribution

It constructs a two-derivative holographic effective action for vector perturbations, incorporating quantum anomalies and analyzing the full Schwinger-Keldysh geometry.

Findings

Boundary current divergence indicates quantum anomaly.

Keldysh functional is unaffected by Chern-Simons term at quadratic order.

Full solution involves complexified radial coordinate and contour integration.

Abstract

We consider a $U(1)$ Maxwell-Chern-Simons theory in $5$-dimensions, and analyze the vector perturbations around a classical charged black-brane background. We solve the equations of motion for these perturbations in a derivative expansion. By computing the boundary current, we find that time and spatial derivatives can be interpreted as the induced electric and magnetic field respectively, and the Chern-Simons term contributes to a nonzero divergence of the boundary current which indicates a quantum anomaly. Using holography, we construct a two-derivative effective action for the vector perturbations. By complexifying the radial coordinate, and using appropriate transformation, we construct the full solution on the complexified bulk contour. By computing the on-shell action for the full Schwinger-Keldysh geometry, we obtain the Keldysh functional. We find that the single boundary on-shell action mixes parity, whereas the Keldysh functional does not depend on the Chern-Simons term up to the quadratic orders in derivative expansion.