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Marginal and irrelevant disorder in Einstein-Maxwell backgrounds

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García-García, AM 


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. Disorder in this case also induces a positive correction to the conductivity. At finite temperature the black hole acquires an effective charge and the thermal conductivity has the expected Drude peak that signals the breaking of translational invariance. However the electric conductivity is not affected by the random chemical potential to leading order in the disorder strength.



hep-th, hep-th, gr-qc

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Physical Review D

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American Physical Society (APS)
Engineering and Physical Sciences Research Council (EP/I004637/1)
A. M. G. thanks Hong Liu and Elias Kiritsis for illuminating discussions. A. M. G. acknowledges partial support from EPSRC, grant No. EP/I004637/1. B. L. thanks Andrew Lucas for interesting discussions and suggestions concerning the conductivity. B.L. is supported by a CAPES/COT grant No. 11469/13-17. Both authors are grateful to the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the completion of this work.