Mutual information as a measure of renormalizability

For decades, renormalization has been an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been thoroughly refined for equilibrium systems, consistently extending it to out-of-equilibrium systems is an important area of research. In this talk, I will present a perturbative analysis of the renormalizability of self-interacting quantum field theories, using quantum mutual information to characterize correlations between infinitesimal shells in momentum space. I will first consider flat spacetime where we introduce dynamics by performing an interaction quench and show that the late-time mutual information relaxes to that for the interacting vacuum and, as a function of shell separation, decays in super-renormalizable theories, saturates in renormalizable (marginal) theories, and grows monotonically in non-renormalizable theories. I will next consider a dynamical spacetime and show that the resulting mutual information has the same qualitative behavior as a function of shell separation. Our results demonstrate that mutual information is a reliable indicator of renormalizability both in and out of equilibrium.