A renormalisation group equation for transport coefficients in (2 + 1)-dimensions derived from the AdS/CMT correspondence

Abstract

Within the framework of the AdS/CMT correspondence asymptotically anti-de Sitter black holes in four space-time dimensions can be used to analyse transport properties in two space dimensions. A non-linear renormalisation group equation for the conductivity in two dimensions is derived in this model and, as an example of its application, both the Ohmic and Hall DC and AC conductivities are studied in the presence of a magnetic field, using a bulk dyonic solution of the Einstein-Maxwell equations in asymptotically AdS4 space-time. The $$ \mathcal{Q} $$ Q -factor of the cyclotron resonance is shown to decrease as the temperature is increased and increase as the charge density is increased in a fixed magnetic field. Likewise the dissipative Ohmic conductivity at resonance increases as the temperature is decreased and as the charge density is increased. The analysis also involves a discussion of the piezoelectric effect in the context of the AdS/CMT framework.

Duality and modular symmetry in the quantum Hall effect from Lifshitz holography

“…However δE ± can be determined from the equations of motion and a radial RG equation for σ ± can be derived. The technical details are left to an appendix, B.1, where the equation in a general dyonic background is derived using the techniques of [55,56] and [57]. The result is given in equation (B.39), Interpreting the classical radial equation of motion as an RG equation was suggested in [58,59] and the relation to the c-theorem was studied in [60,61].…”

“…• We expect a cyclotron resonance with damping, [55,57]. An approximation to the cyclotron resonance can be found provided ω is small and the second term on the right-hand side of (5.20) can be ignored.…”