Drude in D major

We study holographic momentum relaxation in the limit of a large number of spacetime dimensions D. For an axion model we find that momentum conservation is restored as D becomes large. To compensate we scale the strength of the sources with D so that momentum is relaxed even at infinite D. We analytically obtain the quasi-normal modes which control electric and heat transport, and give their frequencies in a 1/D expansion. We also obtain the AC thermal conductivity as an expansion in 1/D, which at leading order takes Drude form. To order 1/D our analytical result provides a reasonable approximation to the AC conductivity even at D=4, establishing large D as a practical method in this context. As a further application, we discuss the signature of the transition from coherent to incoherent behaviour known to exist in the system for finite D.