Deformations of Lifshitz holography

The simplest gravity duals for quantum critical theories with z = 2 'Lifshitz' scale invariance admit a marginally relevant deformation. Generic black holes in the bulk describe the field theory with a dynamically generated momentum scale Λ as well as finite temperature T. We describe the thermodynamics of these black holes in the quantum critical regime where T ≫ Λ². The deformation changes the asymptotics of the spacetime mildly and leads to intricate UV sensitivities of the theory which we control perturbatively in Λ²=T.