Perturbatively charged holographic disorder

Within the framework of holography applied to condensed matter physics, we study a model of perturbatively charged disorder in D =4 dimensions. Starting from initially uncharged AdS₄ , a randomly fluctuating boundary chemical potential is introduced by turning on a bulk gauge field parametrized by a disorder strength V ¯ and a characteristic scale k₀. Accounting for gravitational backreaction, we construct an asymptotically anti-de Sitter (AdS) solution perturbatively in the disorder strength. The disorder averaged geometry displays unphysical divergences in the deep interior. We explain how to remove these divergences and arrive at a well behaved solution. The disorder averaged dc conductivity is calculated and is found to contain a correction to the AdS result. The correction appears at second order in the disorder strength and scales inversely with k₀ . We discuss the extension to a system with a finite initial charge density. The disorder averaged dc conductivity may be calculated by adopting a technique developed for holographic lattices.