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Perturbatively charged holographic disorder

2015; American Physical Society; Volume: 92; Issue: 4 Linguagem: Inglês

10.1103/physrevd.92.046004

1550-7998

D. O’Keeffe, Amanda W. Peet,

Particle physics theoretical and experimental studies

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 ${\mathrm{AdS}}_{4}$, a randomly fluctuating boundary chemical potential is introduced by turning on a bulk gauge field parametrized by a disorder strength $\overline{V}$ and a characteristic scale ${k}_{0}$. 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 ${k}_{0}$. 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.