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Within the framework of the AdS/CMT correspondence asymptotically anti-deSitter black holes in four space-time dimensions can be used to analysetransport properties in two space dimensions. A non-linear renormalisationgroup equation for the conductivity in two dimensions is derived in this modeland, as an example of its application, both the Ohmic and Hall DC and ACconductivities are studied in the presence of a magnetic field, using a bulkdyonic solution of the Einstein-Maxwell equations in asymptotically AdS$_4$space-time. The ${\cal Q}$-factor of the cyclotron resonance is shown todecrease as the temperature is increased and increase as the charge density isincreased in a fixed magnetic field. Likewise the dissipative Ohmicconductivity at resonance increases as the temperature is decreased and as thecharge density is increased. The analysis also involves a discussion of thepiezoelectric effect in the context of the AdS/CMT framework.

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