Integrability in QCD and beyond

Andrei Belitsky, V. M. Braun, A. S. Gorsky, G. P. Korchemsky

Research output: Contribution to journalArticle

110 Citations (Scopus)

Abstract

Yang-Mills theories in four space-time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang-Mills dynamics in several important limits is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations. In this review we explain the general phenomenon of complete integrability and its realization in several different situations. As a prime example, we consider in some detail the scale dependence of composite (Wilson) operators in QCD and super-Yang-Mills (SYM) theories. High-energy (Regge) behavior of scattering amplitudes in QCD is also discussed and provides one with another realization of the same phenomenon that differs, however, from the first example in essential details. As the third example, we address the low-energy effective action in a script N = 2 SYM theory which, contrary to the previous two cases, corresponds to a classical integrable model. Finally, we include a short overview of recent attempts to use gauge/string duality in order to relate integrability of Yang-Mills dynamics with the hidden symmetry of a string theory on a curved background.

Original languageEnglish (US)
Pages (from-to)4715-4788
Number of pages74
JournalInternational Journal of Modern Physics A
Volume19
Issue number28
DOIs
StatePublished - Nov 10 2004

Fingerprint

Yang-Mills Theory
Yang-Mills theory
Integrability
quantum chromodynamics
Yang-Mills
Symmetry
symmetry
Completely Integrable Systems
Complete Integrability
Integrable Models
Spin Chains
Scattering Amplitude
Effective Action
String Theory
scattering amplitude
string theory
High Energy
Gauge
Duality
strings

Keywords

  • Dilatation operator
  • Gauge theories
  • Integrability
  • Regge limit
  • Seiberg-Witten solution

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mathematical Physics
  • Nuclear and High Energy Physics

Cite this

Integrability in QCD and beyond. / Belitsky, Andrei; Braun, V. M.; Gorsky, A. S.; Korchemsky, G. P.

In: International Journal of Modern Physics A, Vol. 19, No. 28, 10.11.2004, p. 4715-4788.

Research output: Contribution to journalArticle

Belitsky, A, Braun, VM, Gorsky, AS & Korchemsky, GP 2004, 'Integrability in QCD and beyond', International Journal of Modern Physics A, vol. 19, no. 28, pp. 4715-4788. https://doi.org/10.1142/S0217751X04019895
Belitsky, Andrei ; Braun, V. M. ; Gorsky, A. S. ; Korchemsky, G. P. / Integrability in QCD and beyond. In: International Journal of Modern Physics A. 2004 ; Vol. 19, No. 28. pp. 4715-4788.
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