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Anomalous transport coefficients from Kubo formulas in Holography

Irene Amado, Karl Landsteiner, Francisco Pena-Benitez

TL;DR

The paper addresses anomaly-induced transport in dense matter by deriving Kubo-type relations for the anomalous magnetic conductivity $\xi_B$ and the anomalous vortical conductivity $\xi_V$ and by interpreting the vortical response as a gravitomagnetic effect. It employs a holographic dual, a 5D Einstein–Maxwell theory with a Chern–Simons term in the RN–AdS background, to compute retarded correlators and extract the conductivities, showing consistency with field-theory results and revealing a new result for $\sigma_V$. A key outcome is the framing of the CVE within a gravitomagnetic context and the introduction of elementary conductivities $\sigma_B$ and $\sigma_V$ that capture the full external-field response. The work enables first-principles CVE calculations across coupling regimes and provides insight into the frequency-dependent behavior of anomalous transport, with potential implications for heavy-ion phenomenology and strongly coupled hydrodynamics.

Abstract

In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magnetic and vortical conductivities. Whereas a Kubo formula for the anomalous magnetic conductivity is well known we develop a new Kubo type formula that allows the calculation of the vortical conductivity through a two point function of the anomalous current and the momentum density. We also point out that the anomalous vortical conductivity can be understood as a response to a gravitomagnetic field. We apply these Kubo formulas to a simple Holographic system, the R-charged black hole.

Anomalous transport coefficients from Kubo formulas in Holography

TL;DR

The paper addresses anomaly-induced transport in dense matter by deriving Kubo-type relations for the anomalous magnetic conductivity and the anomalous vortical conductivity and by interpreting the vortical response as a gravitomagnetic effect. It employs a holographic dual, a 5D Einstein–Maxwell theory with a Chern–Simons term in the RN–AdS background, to compute retarded correlators and extract the conductivities, showing consistency with field-theory results and revealing a new result for . A key outcome is the framing of the CVE within a gravitomagnetic context and the introduction of elementary conductivities and that capture the full external-field response. The work enables first-principles CVE calculations across coupling regimes and provides insight into the frequency-dependent behavior of anomalous transport, with potential implications for heavy-ion phenomenology and strongly coupled hydrodynamics.

Abstract

In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magnetic and vortical conductivities. Whereas a Kubo formula for the anomalous magnetic conductivity is well known we develop a new Kubo type formula that allows the calculation of the vortical conductivity through a two point function of the anomalous current and the momentum density. We also point out that the anomalous vortical conductivity can be understood as a response to a gravitomagnetic field. We apply these Kubo formulas to a simple Holographic system, the R-charged black hole.

Paper Structure

This paper contains 8 sections, 65 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Kubo formulas and constitutive relations
  3. Kubo formulas in Holography
  4. Frequency dependence
  5. Conclusion and Outlook
  6. Second Order Action
  7. Analytic solutions in the hydrodynamic regime
  8. Fluid velocity dependence

Figures (3)

  • Figure 1: Chiral vortical (up) and magnetic (bottom) conductivities as function of the frequency at $\tau=36.5$ (left) and $\tau=0.24$ (right). Red doted points represent real part and thick blue line the imaginary conductivity.
  • Figure 2: Chiral vortical (up) and magnetic (bottom) conductivities as function of the frequency close to $\omega=0$. Real (left) and imaginary (right) part of the normalized conductivity for different values of the dimensionless temperature.
  • Figure 3: Chiral vortical (left) and magnetic (right) conductivities as function of the frequency at $\tau=0.008$. Red doted points represent real part and thick blue line the imaginary conductivity. The real part of $\sigma_V$ at $\omega=0$ is outside the range of the plot.