Character of matter in holography: Spin–orbit interaction

Gauge/Gravity duality as a theory of matter needs a systematic way to characterise a system. We suggest a ‘dimensional lifting’ of the least irrelevant interaction to the bulk theory. As an example, we consider the spin–orbit interaction, which causes magneto-electric interaction term. We show that its lifting is an axionic coupling. We present an exact and analytic solution describing diamagnetic response. Experimental data on annealed graphite shows a remarkable similarity to our theoretical result. We also find an analytic formulas of DC transport coefficients, according to which, the anomalous Hall coefficient interpolates between the coherent metallic regime with ρxx2 and incoherent metallic regime with ρxxρxx as we increase the disorder parameter β. The strength of the spin–orbit interaction also interpolates between the two scaling regimes.