Infrared phases of 2d QCD

TL;DR

This paper classifies 2d QCD theories based on their spectral properties, identifying which develop a mass gap and describing their infrared behavior, including connections to known conformal field theories.

Contribution

It provides a complete list of 2d QCD theories with a mass gap and analyzes their infrared effective theories, including TQFTs and CFTs, with novel insights into anomalies and emergent symmetries.

Findings

Complete classification of gapped 2d QCD theories.

Identification of infrared TQFTs and CFTs for these theories.

Discovery of non-trivial anomalies and emergent supersymmetry in IR.

Abstract

We derive the necessary and sufficient conditions for a 2d QCD theory of massless gluons and left and right chiral quarks in arbitrary representations of a gauge group G to develop a mass gap. These results are obtained from spectral properties of the lightcone and temporal QCD Hamiltonians. The conditions can be explicitly solved, and we provide the complete list of all 2d QCD theories that have a quantum mechanical gap in the spectrum, while any other theory not in the list is gapless. The list of gapped theories includes QCD models with quarks in vector-like as well as chiral representations. The gapped theories consist of several infinite families of classical gauge groups with quarks in rank 1 and 2 representations, plus a finite number of isolated cases. We also put forward and analyze the effective infrared description of QCD - TQFTs for gapped theories and CFTs for gapless theories - and exhibit several interesting features in the infrared, such as the existence of non-trivial global 't Hooft anomalies and emergent supersymmetry. We identify 2d QCD theories that flow in the infrared to celebrated CFTs such as minimal models, bosonic and supersymmetric, and Wess-Zumino-Witten and Kazama-Suzuki models.