Abstract
We construct a top-down holographic model of Weyl semimetal states using (3 + 1)-dimensional mathcal{N} = 4 supersymmetric SU(Nc) Yang-Mills theory, at large Nc and strong coupling, coupled to a number Nf ≪ Nc 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.
Highlights
In lattice systems, the Nielsen-Ninomiya theorem [17] guarantees zero net chirality in the Brillouin zone, or equivalently zero net Chern number
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
In this paper we studied a top-down holographic model of a WSM, namely probe D7-branes in the AdS5 × S5 background of type IIB supergravity, dual to probe hypermultiplets in N = 4 SU(Nc) Yang-Mills (SYM) at large Nc and large coupling λ, with worldvolume fields describing non-zero hypermultiplet mass m and background spatial U(1)A gauge field b
Summary
In type IIB SUGRA in flat space with coordinates x0, x1, . . . , x9, we consider the following SUSY intersection of Nc coincident D3-branes with Nf coincident D7-branes (table 1). In those cases we can “fix the problem,” i.e. prevent the instability, by adding to our ansatz non-zero components of the worldvolume gauge field A These come with their own integration constants, and typically produce additional factors under the square root that can be arranged such that the action remains real. Even if we introduce all components of A in field theory directions, (At(r), Ax(r), Ay(r), Az(r)), the corresponding integration constants cannot be arranged to keep the square root real for all r These integration constants appear in the Legendre-transformed action under the third square root as terms added to those in eq (2.12), but with powers of r sub-leading compared to the pφ term at small r. In appendix A we show that M and the sub-leading asymptotic coefficient C together determine Om as
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