Fermion Interactions and Universal Behavior in Strongly Interacting Theories

TL;DR

This paper explores the universal behavior of strongly interacting fermionic systems using renormalization group techniques, bridging quantum chromodynamics and many-body physics to understand phase transitions and bound-state formation.

Contribution

It provides a comprehensive review of fermionic RG flows and their application to universal phenomena across diverse strongly interacting theories.

Findings

Universal long-range behavior observed in various theories

Renormalization group techniques elucidate phase transition scaling

Connections between QCD and many-body physics are strengthened

Abstract

The theory of the strong interaction, Quantum Chromodynamics (QCD), describes the generation of hadronic masses and the state of hadronic matter during the early stages of the evolution of the universe. As a complement, experiments with ultracold fermionic atoms provide a clean environment to benchmark our understanding of dynamical formation of condensates and the generation of bound states in strongly interacting many-body systems. Renormalization group (RG) techniques offer great potential for theoretical advances in both hot and dense QCD as well as many-body physics, but their connections have not yet been investigated in great detail. We aim to take a further step to bridge this gap. A cross-fertilization is indeed promising since it may eventually provide us with an ab-initio description of hadronization, condensation, and bound-state formation in strongly interacting theories. After giving a thorough introduction to the derivation and analysis of fermionic RG flows, we give an introductory review of our present understanding of universal long-range behavior in various different theories, ranging from non-relativistic many-body problems to relativistic gauge theories, with an emphasis on scaling behavior of physical observables close to quantum phase transitions (i. e. phase transitions at zero temperature) as well as thermal phase transitions.