String Theory seminar - Dong-Gang Wang Seminar

Abstract: Interacting light scalars in de Sitter space (dS) normally lead to infrared (IR) divergences. I shall revisit this topic with recent developments of the cosmological bootstrap: At the tree level, we first see that massive exchange diagrams are IR-finite, and conformal Ward identities lead to the boundary differential equations, which in the end allows us to bootstrap a full set of cosmological collider non-Gaussianity. While for massless exchanges, IR divergences are normally expected, and then the boundary differential equations become the ones from anomalous conformal Ward identities. This leads to a full classification for non-Gaussianities from multi-field inflation. At the loop level, we apply the wavefunction method, and identify that the leading contributions to IR-divergent correlators always come from classical loops with tree-level wavefunction coefficients. This significantly simplifies the problem and indicates the importance of the saddle-point approximation when we go beyond perturbation theory. With the new insight, we present a non-perturbative derivation of the stochastic formalism. Using the semi-classical wavefunction, we find that the Fokker-Planck equation follows as a consequence of the Schroedinger equation and the Polchinski's equation for the exact renormalization group flow.