Week 19.06.2023 – 25.06.2023

Single field models of inflation capable to produce primordial black holes usually require a significant departure from the standard, perturbative slow-roll regime. In fact, in many of these scenarios, the size of the slow-roll parameter eta becomes larger than one during a short phase of inflationary evolution. In order to develop an analytical control on these systems, I explore the limit of eta large, and promote 1/eta to a small quantity to be used for perturbative expansions. Formulas simplify, and analytic expressions for the two and three point functions of curvature fluctuations are obtained. I will then discuss the behaviour of loop corrections to inflationary observables in this framework

Based on 2306.05551 with Ankur and D. Carmi. Studying QFT in AdS allows to translate phenomena in massive QFT in the bulk to properties of the boundary conformal correlators. I will illustrate this in the example of a strongly coupled gauge theory, namely scalar QED in dimension D<4. The tool that I will use to compute is the large N expansion, where N is the number of flavors. I will show that the four-point function of the charged operator dual to the scalar electrons can be computed exactly in the coupling at leading order at large N, both in the Coulomb and in the Higgs phase, and explain its salient properties. Finally I will discuss an IR divergence present in integer dimension D=3 that signals the breaking of the AdS isometries due to a boundary running coupling.