Non-linear, Finite Frequency Quantum Critical Transport from AdS/CFT

Abstract

Transport at a quantum critical point depends sensitively on the relative magnitudes of temperature, frequency and electric field. Here we used the gauge/gravity correspondence to compute the full temperature and, generally nonlinear, electric field dependence of the electrical conductivity for some model critical theories. In the special case of 2+1 dimensions we are also able to find the full time-dependent response of the system to an arbitrary time dependent external electric field. The response of the system is instantaneous, implying a frequency independent conductivity. We describe a mechanism that rationalizes the instantaneous response.Comment: 16 pages; v2: minor typos fixed and ref added; v3: typo fixed and discussion of S-duality clarified and expande