Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography

TL;DR

This paper reviews various methods for computing fermion propagators in strongly correlated systems with overdamped bosonic modes, highlighting conflicts and gaps in current approaches and emphasizing the need for a definitive solution.

Contribution

It critically compares existing approaches like diagrammatic resummation, bosonization, and holography, revealing their limitations in addressing non-Fermi liquid behavior.

Findings

Existing methods often conflict or are incomplete

Current approaches do not fully resolve fermion propagator calculations

A comprehensive solution to the problem remains elusive

Abstract

This note addresses the problem of computing fermion propagators in a broad variety of strongly correlated systems that can be mapped onto the theory of fermions coupled to an (over)damped bosonic mode. A number of the previously applied approaches and their results are reviewed, including the conventional diagrammatic resummation and eikonal technique, as well as the 'experimental' higher dimensional bosonization and generalized (i.e., 'bottom-up' or 'non-AdS/non-CFT') holographic conjecture. It appears that, by and large, those results remain either in conflict or incomplete, thereby suggesting that the ultimate solution to this ubiquitous problem is yet to be found.