I will describe thermodynamics and calculation of real time correlators in CFTs with extended W-symmetries, dual to AdS_3 gravity with a finite number of higher spin fields. I will point out mechanisms, including the appearance of a novel effective temperature, by which the proposed chaos bound due to Maldacena-Shenker-Stanford is violated in these theories.

We discuss examples of relevant deformations of known CFTs placed in de Sitter spacetime, possessing AdS gravity duals with Big Crunch singularities. We point out generic aspects of such dual backgrounds, including the behaviour in the vicinity of the singularity, holographic correlators in the geodesic approximation, and retarded correlators in an analytically tractable example within the AdS_4/CFT_3 context. We briefly describe an attempt to characterise the bulk crunch and its putative resolution within the O(N) vector model in 3D.

We show that certain exactly marginal and relevant deformations of N=4 theory which preserve N=1 supersymmetry, exhibit rich infrared dynamics. These theories have moduli spaces with discrete (Higgs) branches. On certain branches the theory flows to the Klebanov-Witten conifold SCFT, while on other branches the theory undergoes a Seiberg duality cascade terminating in an N=1 theory with a mass gap. Using the matrix model approach the quantum moduli spaces and quantum superpotentials of these theories can be computed exactly. In the D-brane picture these quantum moduli spaces correspond to the Calabi-Yau space in the geometric dual description of the gauge theory.