# Recent Developments in Non-Fermi Liquid Theory

## TL;DR

This review discusses recent theoretical advances in understanding non-Fermi liquids in two dimensions, focusing on perturbative and non-perturbative approaches to their universal low-energy physics.

## Contribution

It introduces and compares two recent methods—dimensional regularization and interaction-driven scaling—for analyzing non-Fermi liquids in two dimensions.

## Key findings

- Controlled perturbative analysis via dimensional regularization.
- Exact treatments of strongly coupled non-Fermi liquids using interaction-driven scaling.
- Identification of universal properties in non-Fermi liquids.

## Abstract

Non-Fermi liquids arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticle, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the number of co-dimensions of Fermi surface. The second is a non-perturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.