Weyl Semimetals and Holography, with a hint of Massive Spinors

Abstract

The AdS/CFT correspondence relates a weakly interacting gravity theory in a D+1-dimensional anti-de Sitter (AdS) bulk spacetime to a strongly interacting conformal field theory (CFT) on the boundary of the D-dimensional boundary of the AdS bulk. The correspondence potentially enables us to perform computations in strongly interacting condensed matter systems where regular perturbation theory breaks down. We are especially interested in the system of Weyl semimetals, a gapless semiconductor with touching valence and conduction bands based on two-component chiral fermions which in the non-interacting limit satisfy the Weyl equation. This system exhibits the anomalous Hall effect when time-reversal symmetry is broken. This adds contributions to the conductivity of the system. We compare i) the contributions to the conductivity and ii) the spectral functions of the interacting and non-interacting case. Moreover we make a beginning for the study of a system of non-relativistic massive fermions interacting via AdS/CFT.