Universite Paris Diderot
Curved holographic RG flows, quantum phase transitions and AdS vacuum decay
I will discuss recent developements in the holographic descriptions of Renormalization Group flows of quantum field theories on curved space-times. On the gravity side I will consider is Einstein gravity coupled to a scalar field. On the field theory side, the latter is dual to a relevant operator which drives the RG flow. In this context, I will discuss solutions in which the transverse slices to the holographic direction are curved, and in particular maximally symmetric spaces. In the case of positive curvature, these solutions correspond to RG flows of field theories on a sphere or de Sitter space. I will present situations in which quantum phase transitions driven by curvature arise. Furthermore, these Euclidean geometries may be seen as gravitational instantons which mediate vacuum tunneling. This will lead to a discussion of AdS vacuum decay in Einstein-scalar theories.