Exotic renormalisation group flows from black holes

Abstract

In this thesis we construct a variety of black hole solutions that have planar horizons and are asymptotically Anti-de Sitter, thus relevant in the context of the gauge/gravity correspondence. We use the correspondence to investigate the renormalisation group flows of the corresponding dual field theories. Our solutions break translations along one or more spatial directions of the dual field theory, thus making them suitable for describing lattices in strongly coupled matter. After a brief introduction to the gauge/gravity duality, three different set-ups are considered. First, in the context of type IIB supergravity, our solutions are dual to anisotropic plasmas that arise from deforming an infinite family of CFTs. Second, we construct black holes in D = 11 supergravity, making our solutions relevant for ABJM theory. And finally, we take a bottom-up approach, designing a gravity model for which the black hole solutions allow us to model interesting phase transitions that are triggered by the strong breaking of translational invariance.

In each scenario, we observe boomerang-like RG flows, in which the UV fixed point reappears as the IR fixed point. Similarly, all of our constructions reveal one or more intermediate scaling regimes, and we show how this can affect the scaling of some transport coefficients. For the phenomenological boomerang flows, we show that the entropic c-function is not monotonic. Furthermore, this model will reveal a novel thermal insulating ground state that has non-power-law scaling. The relation between the thermal diffusivity and butterfly velocity of these novel ground states is also studied.