Higher Representations and Quark Confinement

TL;DR

This paper explores how higher-categorical representation theory can distinguish confined and Higgs phases in scalar QCD at zero temperature, based on their spectral organization and baryon charge properties.

Contribution

It introduces a novel approach using higher-categorical representation theory to differentiate phases of scalar QCD without relying on 1-form symmetries.

Findings

Confined phase allows only particles with integer baryon charges.

Higgs phase features coexistence of quarks and vortices with Aharonov-Bohm effects.

Spectral organization differs between phases, revealing their distinct nature.

Abstract

The concept of a (de)confined phase in QFT is well-defined in the presence of $1$-form symmetries and their spontaneous symmetry breaking. However, in scenarios where such symmetries are absent, confinement is not a well-defined phase property. In this work, we propose that, when restricting to a specific submanifold of the parameter space -- namely at zero temperature and fixed quark mass -- the confined and adjoint Higgs phases of scalar QCD can be distinguished through the different organization of their spectra, as seen from the perspective of the baryon symmetry. The analysis is performed in terms of an appropriate higher-categorical representation theory, recently developed for generalized symmetries. Consistent with expectations, we find that the confined phase permits only particles with integer baryon charges, while the Higgs phase is characterized by the coexistence of bare quarks and center vortices, exhibiting a non-trivial Aharonov-Bohm effect between these excitations.