Skip to main content

What Is Confinement?

  • Chapter
  • First Online:
An Introduction to the Confinement Problem

Part of the book series: Lecture Notes in Physics ((LNP,volume 972))

  • 823 Accesses


Confinement and symmetry. Linear Regge trajectories, the linear static quark potential, and the “spinning stick” model. String breaking, existence of “color confinement” in the Higgs phase, and the difficulty of associating confinement with an unbroken or spontaneously broken remnant gauge symmetry. Confinement as magnetic disorder; center symmetry as the global symmetry corresponding to the confined phase.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


  1. 1.

    What this means is that the order parameter for the transition can be non-zero in the infinite 3-volume limit at any fixed time, but have different values at different times, averaging to zero if we average over all times. Thus the symmetry can be spontaneously broken on any single timeslice, or finite set of timeslices, without violating the Elitzur theorem.

  2. 2.

    The Clay Mathematics Institute offers a large cash prize ( for proving that Yang-Mills theory has a mass gap, which would be true in any gauge theory which is in either a magnetically disordered phase, as in pure Yang-Mills theory, or a massive phase, as in Higgs theories and in real QCD.


  1. G. Bali, QCD forces and heavy quark bound states. Phys. Rep. 343, 1 (2001). arXiv: hep-ph/0001312

    Google Scholar 

  2. O. Philipsen, H. Wittig, String breaking in non-Abelian gauge theories with fundamental matter fields. Phys. Rev. Lett. 81, 4056 (1998). Erratum-ibid. 83, 2684 (1999). arXiv:hep-lat/9807020

    Google Scholar 

  3. F. Knechtli, String breaking and lines of constant physics in the SU(2) Higgs model. Nucl. Phys. Proc. Suppl. 83, 673 (2000). arXiv:hep-lat/9909164

    Google Scholar 

  4. C.E. Detar, U.M. Heller, P. Lacock, First signs for string breaking in two-flavor QCD. Nucl. Phys. Proc. Suppl. 83, 310 (2000). arXiv:hep-lat/9909078

    Google Scholar 

  5. E. Fradkin, S. Shenker, Phase diagrams of lattice gauge theories with Higgs fields. Phys. Rev. D 19, 3682 (1979)

    Article  ADS  Google Scholar 

  6. K. Osterwalder, E. Seiler, Gauge field theories on the lattice. Ann. Phys. 110, 140 (1978)

    Article  MathSciNet  Google Scholar 

  7. C. Lang, C. Rebbi, M. Virasoro, The phase structure of a non-Abelian gauge Higgs system. Phys. Lett. 104B, 294 (1981)

    Article  ADS  Google Scholar 

  8. C. Bonati, G. Cossu, M. D’Elia, A. Di Giacomo, Phase diagram of the lattice SU(2) Higgs model. Nucl. Phys. B 828, 390 (2010). arXiv:0911.1721 [hep-lat]

    Google Scholar 

  9. J. Frohlich, G. Morchio, F. Strocchi, Higgs phenomenon without symmetry breaking order parameter. Nucl. Phys. B 190, 553 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  10. G. ’t Hooft, Which topological features of a gauge theory can be responsible for permanent confinement?. NATO Sci. Ser. B 59, 117 (1980)

    Google Scholar 

  11. A. Maas, R. Sondenheimer, P. Törek, On the observable spectrum of theories with a Brout?Englert?Higgs effect. Ann. Phys. 402, 18 (2019). arXiv:1709.07477 [hep-ph]

  12. T. Kugo, I. Ojima, Local covariant operator formalism of nonabelian gauge theories and quark confinement problem. Prog. Theor. Phys. Suppl. 66, 1 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  13. T. Kugo, The Universal Renormalization Factors Z(1) / Z(3) and Color Confinement Condition in nonAbelian Gauge Theory. arXiv:hep-th/9511033

    Google Scholar 

  14. E. Marinari, M.L. Paciello, G. Parisi, B. Taglienti, The string tension in gauge theories: a Suggestion for a new measurement method. Phys. Lett. B 298, 400 (1993). arXiv:hep-lat/9210021

    Google Scholar 

  15. L. Del Debbio, A. Di Giacomo, G. Paffuti, Detecting dual superconductivity in the ground state of gauge theory. Phys. Lett. B 349, 513 (1995). arXiv:hep-lat/9403013

    Google Scholar 

  16. A. Di Giacomo, B. Lucini, L. Montesi, G. Paffuti, Color confinement and dual superconductivity of the vacuum. 1. Phys. Rev. D 61, 034503 (2000). arXiv:hep-lat/9906024

    Google Scholar 

  17. H. Hata, Restoration of the local gauge symmetry and color confinement in non-Abelian gauge theories. II. Prog. Theor. Phys. 69, 1524 (1983). Prog. Theor. Phys. 67, Restoration of the local gauge symmetry and color confinement In non-Abelian gauge theories, 1607 (1982)

    Google Scholar 

  18. R. Alkofer, C.S. Fischer, F.J. Llanes-Estrada, K. Schwenzer, The quark-gluon vertex in Landau gauge QCD: its role in dynamical chiral symmetry breaking and quark confinement. Ann. Phys. 324, 106 (2009). arXiv:0804.3042 [hep-ph]

    Google Scholar 

  19. H. Nakajima, S. Furui, A. Yamaguchi, In: Proceedings of the 30th International Conference on High-Energy Physics (ICHEP 2000). Numerical study of the Kugo-Ojima criterion and the Gribov problem in the Landau gauge. arXiv:hep-lat/0007001

    Google Scholar 

  20. J. Greensite, S. Olejnik, D. Zwanziger, Coulomb energy, remnant symmetry, and the phases of non-Abelian gauge theories. Phys. Rev. D 69, 074506 (2004). arXiv:hep-lat/0401003

    Google Scholar 

  21. W. Caudy, J. Greensite, On the ambiguity of spontaneously broken gauge symmetry. Phys. Rev. D 78, 025018 (2008). arXiv:0712.0999 [hep-lat]

    Google Scholar 

  22. J. Greensite, B. Lucini, Is confinement a phase of broken dual gauge symmetry? Phys. Rev. D 78, 085004 (2008). arXiv:0806.2117 [hep-lat]

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Greensite, J. (2020). What Is Confinement?. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 972. Springer, Cham.

Download citation

Publish with us

Policies and ethics