A Weyl semimetal from AdS/CFT with flavour

Abstract

We construct a top-down holographic model of Weyl semimetal states using (3 + 1)-dimensional N = 4 supersymmetric SU(Nc) Yang-Mills theory, at large Nc and strong coupling, coupled to a number Nf ≪ Nc of 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.