Affine Algebras and Strong Interaction Theories

  • L. Dolan
Part of the Progress in Physics book series (PMP, volume 8)


A new infinite parameter symmetry, the Kac-Moody Lie algebras, appears in several different connections with theories of the strong Interactions. Its explicit representation in terms of the dual string is reviewed here in simple language. A nonlocal nonlinear realization of a subalgebra of the affine algebras on the self-dual class of solutions of the Yang Mills theory is also reviewed. It is remarked that this structure occurs naturally in a Kaluza-Klein search for the new symmetry on the full gauge theory. The existence of the same invariance in these different models of the hadrons may serve to unify the descriptions and lead to solvability in the nonperturbative regime.


Gauge Theory Yang Mill Theory Vertex Operator Dual String Nonperturbative Regime 
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  1. [1]
    I. Dolan, “Kac-Moody Algebras and Exact Solvability in Hadronic Physics”, to be published in Physics Reports; and references therein.Google Scholar
  2. [2]
    L. Dolan, “Kaluza-Kloin Theories as a Tool to Find New Gauge Theory Symmmetries”, to be published in the Proceedings of Orbis Scientiae 1983, Coral Gables.Google Scholar
  3. [3]
    I.B. Frenkel and V.G. Kac, Inv. Math. 62, 23 (1980); J. Lepowsky and R.L. Wilson, Com. HathTPhys. 62, 43 (1978).CrossRefGoogle Scholar
  4. [4]
    For more expository papers, see also I.B. Frenkel, “Representations of Kac-Moody algebras and Dual Resonance Models”, Princeton preprint and J. Lepowsky, “Some Constructions of the affine Lie algebra A1. (1)”, Rutgers preprint.Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • L. Dolan
    • 1
  1. 1.The Rockefeller UniversityNew YorkUSA

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