Marginal and Irrelevant Disorder in Einstein-Maxwell backgrounds

Understand

We study analytically the effect of a weak random chemical potential of zero average in an Einstein-Maxwell background.

• For uncorrelated disorder this perturbation is relevant however we show that it can become marginal or even irrelevant by tuning disorder correlations.
• At zero temperature we find that, to leading order in the disorder strength, the correction to the conductivity for irrelevant perturbations vanishes.
• In the marginal case, in order to renormalize a logarithmic divergence, we carry out a resummation of the perturbative expansion of the metric that leads to a Lifshitz-like geometry in the infrared.