Effective Gauge Theories, The Renormalization Group, and High-Temperature Superconductivity

TL;DR

This paper introduces the renormalization group approach to effective field theories with a focus on Fermi surface systems, explaining quasiparticles and applying these ideas to high-temperature superconductivity and gauge theories.

Contribution

It connects renormalization group methods with large-N_f treatments and applies this framework to understand non-Fermi liquid behavior in high-T_c superconductors.

Findings

Finite temperature resistivity shows O(1/N_f) corrections to linear T behavior.

Scaling corrections align with experimental deviations from Fermi liquid theory.

Application to 3D U(1) gauge theory reveals non-trivial infrared structure.

Abstract

These lectures serve as an introduction to the renormalization group approach to effective field theories, with emphasis on systems with a Fermi surface. For such systems, demanding appropriate scaling with respect to the renormalization group for the appropriate excitations leads directly to the important concept of quasiparticles and the connexion between large-N_f treatments and renormalization group running in theory space. In such treatments N_f denotes the number of effective fermionic degrees of freedom above the Fermi surface; this number is roughly proportional to the size of the Fermi surface. As an application of these ideas, non-trivial infra red structure in three dimensional U(1) gauge theory is discussed, along with applications to the normal phase physics of high-T_c superconductors, in an attempt to explain the experimentally observed deviations from Fermi liquid behaviour. Specifically, the direct current resistivity of the theory is computed at finite temperatures, $T$, and is found to acquire $O(1/N_f)$ corrections to the linear $T$ behaviour. Such scaling corrections are consistent with recent experimental observations in high T_c superconducting cuprates.