Optical Conductivity in the Cuprates and Gauge/Gravity duality

The recent claim that inhomogeneous charge densities in a bulk gravitational setting are capable of yielding power law optical conductivities observed in the cuprates is examined critically. We first show that charge density in the Q-lattice proposal by Donos et al. [1] is actually homogeneous and hence is not a satisfactory candidate for addressing this issue. We then construct a two-scalar field system that can interpolate between the holographic lattice of Horowitz et al. [2] and the Q-lattice of Donos et al. and explore how the power law in the optical conductivity turns on as a function of the inhomogeneity and the mixing of higher harmonics. \\[4pt] [1] A. Donos and J. P. Gauntlett, ``Holographic Q-lattices,'' JHEP 1404 (2014) 040, arXiv:1311.3292 [hep-th].\\[0pt] [2] G. T. Horowitz, J. E. Santos, and D. Tong, ``Optical Conductivity with Holographic Lattices,'' JHEP 1207 (2012) 168, arXiv:1204.0519 [hep-th].