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Higher Representations and Quark Confinement

Finn Gagliano, Andrea Grigoletto, Kantaro Ohmori

TL;DR

This work develops a higher-categorical framework based on higher strip algebras to classify (de)confinement in gauge theories beyond the traditional Landau paradigm, focusing on scalar QCD at zero temperature and fixed mass. By analyzing RG flow via a Bockstein-induced pullback between symmetry categories, it reveals that confinement yields only baryonic IR content while adjoint Higgs phases host bare quarks and center vortices with Aharonov-Bohm interactions, and these sectors become equivalent under gauging of higher-form symmetries. The key contributions include explicit identifications: in pure Yang–Mills, Rep_{conf} = 3Rep(Z_N^{[1]}) and Rep_{Higgs} = 3Vec(Z_N^{[1]}), with a corresponding interpretation of confining strings and center vortices; in scalar QCD, the pullback formalism shows how quarks and baryons reorganize under the deeper UV symmetry, associating AB phases with center vortices. Overall, the paper provides a systematic, higher-categorical method to diagnose and relate confinement, Higgs regimes, and the spectrum of excitations across RG flow, with potential applications to broader theories and higher-dimensional generalized symmetries.

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.

Higher Representations and Quark Confinement

TL;DR

This work develops a higher-categorical framework based on higher strip algebras to classify (de)confinement in gauge theories beyond the traditional Landau paradigm, focusing on scalar QCD at zero temperature and fixed mass. By analyzing RG flow via a Bockstein-induced pullback between symmetry categories, it reveals that confinement yields only baryonic IR content while adjoint Higgs phases host bare quarks and center vortices with Aharonov-Bohm interactions, and these sectors become equivalent under gauging of higher-form symmetries. The key contributions include explicit identifications: in pure Yang–Mills, Rep_{conf} = 3Rep(Z_N^{[1]}) and Rep_{Higgs} = 3Vec(Z_N^{[1]}), with a corresponding interpretation of confining strings and center vortices; in scalar QCD, the pullback formalism shows how quarks and baryons reorganize under the deeper UV symmetry, associating AB phases with center vortices. Overall, the paper provides a systematic, higher-categorical method to diagnose and relate confinement, Higgs regimes, and the spectrum of excitations across RG flow, with potential applications to broader theories and higher-dimensional generalized symmetries.

Abstract

The concept of a (de)confined phase in QFT is well-defined in the presence of -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.
Paper Structure (9 sections, 29 equations, 4 figures, 1 table)

This paper contains 9 sections, 29 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Higher Strip Algebras
  3. Review of (1+1)-dimensions
  4. Strip algebras in (d+1)-dimensions
  5. Phases of Yang-Mills Theory
  6. Scalar QCD
  7. Review of Categorical Symmetry
  8. RG Flow Symmetry Homomorphism
  9. Inner Structure of Baryons

Figures (4)

  • Figure 1: A $1$-morphism $(a,p,q,n,m,\alpha,\beta)$ of the strip algebra between the objects $(U_i,P_i,Q_i,R_i,S_i,v_i,w_i)_{i=1,2}$.
  • Figure 2: Inner structure of a baryon with its $p$-valent junction.
  • Figure :
  • Figure :