UNC-CH Physics and Astronomy PhD Dissertation Defense 

Ramón Fowler

“Information Theoretic Interpretations of Renormalization Group Flow”

We interpret the renormalization group flow between quantum field theories as a communication channel problem, which allows us to quantify UV-IR mixing in terms of information theoretic quantities, i.e., we can quantify the information of the UV theory that remains accessible in the IR theory. Because of the AdS-CFT interpretation of the renormalization group flow, our interpretation applies to the AdS-CFT correspondence too. To make this interpretation, we make use of the Kullback-Leibler (KL) divergence, which quantifies the information theoretic distance between two probability distributions. We study the probability distributions associated with Euclidean quantum field theories; the KL divergence thus computes the relative entropy between these Euclidean quantum field theories, as in statistical field theory. We then use the renormalization group and the techniques of effective field theory to find the probability distributions that we need to use with the KL divergence in order to measure the information lost upon performing the renormalization group transformation. We compute the KL divergence for a few example toy models, mostly Ising models.