Membrane paradigm and RG flows for anomalous holographic theories

TL;DR

This paper explores how holographic RG flows and membrane paradigm techniques can be used to understand anomalous transport phenomena in holographic theories with gauge and gravitational anomalies, even with higher derivative complexities.

Contribution

It demonstrates the derivation of conservation laws and membrane currents in anomalous holographic theories, including those with gravitational anomalies and higher derivatives.

Findings

Conservation laws can be established despite gauge invariance breaking by Chern-Simons terms.

Membrane currents at the horizon characterize anomalous transport.

Higher derivatives in gravitational anomalies influence membrane current construction.

Abstract

Holographic RG flows can be better understood with the help of radially conserved charges. It was shown by various authors that the bulk gauge and diffeomorphism symmetries lead to the conservation of the zero mode of the holographic U(1) current and, if the spacetime is stationary, to that of the holographic heat current. In describing dual theories with \'t Hooft anomalies the bulk gauge invariance is broken by Chern-Simons terms. We show that conservation laws can still be derived and used to characterize the anomalous transport in terms of membrane currents at the horizon. We devote particular attention to systems with gravitational anomalies. These are known to be problematic due to their higher derivative content. We show that this feature alters the construction of the membrane currents in a way which is deeply tied with the anomalous gravitational transport.