Anomaly induced transport from symmetry breaking in holography

TL;DR

This work investigates how quantum anomalies induce transport in relativistic fluids when symmetries are explicitly broken, using a holographic 5D Einstein–Maxwell model with pure and mixed Chern–Simons terms and a symmetry-breaking scalar. By including full backreaction and employing Kubo formulae, it shows that anomaly‑induced transport can extend to non‑anomalous sectors, with all conductivities sensitively depending on the symmetry-breaking parameter $M$ and the chemical potentials $\,\mu_v$, $\,\mu_a$, and $\,\mu_w$. The authors derive analytic large‑$M$ limits and validate them against full numerics, revealing redistribution of magnetic responses from axial to non‑anomalous sectors as symmetry breaking grows. These results illuminate the role of mixed gauge–gravitational anomalies in holographic transport and suggest observable consequences in strongly coupled systems with broken symmetries, with potential implications for condensed matter contexts such as valley currents in Weyl materials.

Abstract

We study the transport properties of relativistic fluids induced by quantum anomalies in presence of explicit symmetry breaking. To this end we consider a holographic Einstein-Maxwell model in 5 dimensions with pure gauge and a mixed gauge-gravitational Chern-Simons terms, coupled with a scalar field. To study the chiral vortical effects and the energy transport sector, apart from the chiral magnetic effects, we have considered the full backreaction of the gauge field on the metric. We have studied the anomalous effects by using Kubo formulae involving correlators of the charged currents and the energy current. Our findings reveal that, in the presence of explicit symmetry breaking, anomaly-induced transport phenomena can extend beyond anomalous currents and affect non-anomalous sectors as well. In particular, we find that all the conductivities display a distinct sensitivity to the mass parameter controlling the symmetry breaking, thus reflecting the interplay between anomaly coefficients and explicit symmetry breaking terms. These findings highlight the role played by pure gauge and mixed gauge-gravitational anomalies in holographic transport, and their importance for strongly coupled systems with broken symmetries.

Figures (21)

• Figure 1: Plot showing the dependence of the background with $u$. Color code: Blue - $f(u)$, Orange - $A_{t+} (u)$, and Green - $V_t(u)$ (left panel); Blue - $e^{\chi(u)}$, Orange - $\phi(u) / \sqrt{u}$, and Green - $A_{t-} (u)$ (right panel). We have set $\mu_v = 0.1$, $\mu_a=0.3$, $\mu_w=0.2$ and $M=0.6$.
• Figure 2: Plots of the conductivities $\sigma^{B}_{v v} = \sigma^{B}_{a a}$ and $\sigma^{B}_{v a} =\sigma^{B}_{a v}$ in the massless case $(M = 0)$ as a function of $\mu_a/(\pi T)$. Solid red lines correspond to the analytic results of (\ref{['eq:sigmaAB_ana']})-(\ref{['eq:sigmaAV_ana']}), while blue dots stand for the numerical results computed by using the method of sec. \ref{['subsec:numerical_method']}. We have set $\mu_v/(\pi T)=0.1$.
• Figure 3: Plots of the conductivities $\sigma^{B}_{\varepsilon v} = \sigma^{V}_{v}$ and $\sigma^{B}_{\varepsilon a} = \sigma^{V}_{a}$ in the massless case $(M = 0)$ as a function of $\mu_a/(\pi T)$. See fig. \ref{['fig:coryvM0']} for further details.
• Figure 4: Plot of the conductivity $\sigma^{V}_{\varepsilon}$ in the massless case $(M = 0)$ as a function of $\mu_a/(\pi T)$. See fig. \ref{['fig:coryvM0']} for further details.
• Figure 5: Case 1: Plots of the conductivities $\sigma^B_{s v}$, where $s \in \{ v, a, w, \varepsilon \}$ as a function of $\mu_v/(\pi T)$. We have set $\mu_a/(\pi T)=0.3$ and $\mu_w/(\pi T)=0.2$.