Conductivities and excitations of a holographic flavour brane Weyl semimetal

We compute the electrical conductivities at non-zero frequency in a top-down holographic model of a Weyl semimetal, consisting of $\mathcal{N}=4$ supersymmetric $\mathrm{S}\mathrm{U}(N_c)$ Yang–Mills theory coupled to $\mathcal{N}=2$ hypermultiplets with mass $m$, subject to an applied axial vector field $b$. The model exhibits a first-order phase transition between a Weyl semimetal phase at small $m\mathrm{/}b$ and an insulating phase at large $m\mathrm{/}b$. The conductivities develop peaks and troughs as functions of real frequency at low temperatures and for $m\mathrm{/}b$ close to the phase transition. We compute the poles of the conductivities as functions of complex frequency, finding poles with small imaginary part at low temperatures and close to the phase transition.