Towards non-AdS holography via solvable irrelevant deformations

It is widely believed that quantum gravity is holographic, namely that it admits a description in terms of a lower-dimensional, non-gravitational theory. The AdS/CFT correspodence, which relates quantum gravity in certain hyperbolic space-times (AdS) to conformal field theories (CFTs - a special kind of local quantum field theories) in one dimension less is a very concrete and highly successful realisation of this idea. Extending the holographic  correspondence to non-AdS backgrounds has however proven to be difficult. In this talk, I will argue that at least in certain cases of interest, the holographically dual quantum field theories correspond to special kinds of irrelevant deformations of a CFT, which are finely-tuned to yield a theory that is UV-complete, yet fundamentally non-local. I will then discuss a set of exactly solvable such  irrelevant deformations of two-dimensional CFTs and show that, despite their non-locality, the deformed theories still possess Virasoro symmetry and correlation functions that are entirely determined by those of the undeformed CFT. Time permitting, I will discuss potential applications of these solvable models to non-AdS holography.