I will discuss the two-dimensional O(n) model for a continuous range of n. It can be defined non-perturbatively for any n as an infrared limit of certain lattice loop models, which in the IR give rise to two families of CFTs. For n<2 these CFTs are logarithmic, while for n>2 they are also complex. For n<2 the RG flow to the fixed points violates the straightforward notion of naturalness and appears tuned.

I will discuss the tools we are developing to calculate correlation functions of primordial inflationary perturbations. In this talk, we will focus on the limit where gravitational excitations are neglected and the cosmological spacetime is assumed to be exactly de Sitter. Even in this simplifying limit, which corresponds to a Quantum Field Theory on a de Sitter background, very few examples of explicit analytic calculations exist and little is known about basic properties of the correlators. I will show that for any dS QFT there exists a theory formulated in a Euclidean Anti-de SItter space and which reproduces all the correlation functions. This leads to major technical simplifications and allows to demonstrate various analytic properties of the cosmological observables. Understanding of these properties has both phenomenological applications in inflation, as well as provides some hints about more fundamental description for cosmological spacetimes. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]