A Weyl Semimetal from AdS/CFT with Flavour

TL;DR

This paper develops a holographic model of Weyl semimetals using string theory techniques, revealing a first-order quantum phase transition characterized by anomalous Hall conductivity that is tied to the axial anomaly.

Contribution

It introduces a top-down holographic construction of Weyl semimetals within a supersymmetric gauge theory framework, connecting phase transitions to anomaly-related transport properties.

Findings

Identifies a first-order quantum phase transition driven by mass and axial field.

Shows anomalous Hall conductivity is fixed by the axial anomaly, independent of mass.

At finite temperature, the transition persists with modified Hall response.

Abstract

We construct a top-down holographic model of Weyl semimetal states using $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills theory, at large $N_c$ and strong coupling, coupled to a number $N_f \ll N_c$ of $\mathcal{N}=2$ hypermultiplets with mass $m$. A $U(1)$ subgroup of the R-symmetry acts on the hypermultiplet fermions as an axial symmetry. In the presence of a constant external axial gauge field in a spatial direction, $b$, we find the defining characteristic of a Weyl semi-metal: a quantum phase transition as $m/b$ increases, from a topological state with non-zero anomalous Hall conductivity to a trivial insulator. The transition is first order. Remarkably, the anomalous Hall conductivity is independent of the hypermultiplet mass, taking the value dictated by the axial anomaly. At non-zero temperature the transition remains first order, and the anomalous Hall conductivity acquires non-trivial dependence on the hypermultiplet mass and temperature.