Optical Conductivity in Holography with Hyperscaling Violation and Massive Gravity

One of the long-standing enigmas in the field of strongly-interacting electron systems is the mid-frequency power law form of the optical conductivity in the cuprates, $|\sigma| \sim \omega^{-\alpha}$. Many efforts have been put forth to obtain this power law using the AdS/CFT correspondence while maintaining the experimentally observed Drude form of the conductivity at low frequency. Some models have obtained the power law form over a very narrow range but none have matched the robust form lasting over decades as in experimental observations. We expand on previous constructions by introducing the dynamical exponent $z$ and hyperscaling parameter $\theta$ in a theory that breaks translational invariance using massive gravity. We seek a form of the optical conductivity that reproduces the functional form of the cuprates over all frequency regimes.