nLab
large N limit

In theoretical physics, one often considers gauge theory models whose symmetries are groups of large matrices, e.g. U(N)U(N) or O(N)O(N). The limit of such theories for NN\to \infty has often remarkable properties and string-like features.

This limit is sometimes appearing in its own right, but sometimes it is just considered as an approximation for a system with fixed finite NN. One of the features is that in the large N limit is that non-planar Feynman diagrams loose their importance and that the correlation functions satisfy certain decoupling/factorization rule. The behaviour is studied in terms of expansion in 1/N1/N whose square has a simialr role to Planck constant in semiclassical approximation limit of quantum mechanics.

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  • Laurence G. Yaffe, Large N limits as classical mechanics, Rev. Mod. Phys. 54, 407–435 (1982) pdf
  • G ‘t Hooft, A planar diagram theory for strong interactions, Nuclear Physics B 72, 3 (1974), 461-473, doi
  • G. ‘t Hooft, Large N, workshop lecture, hep-th/0204069
  • S. Coleman, 1/N, in Aspects of Symmetry, Cambridge University Press 1985.
  • A. V. Manohar, Large N QCD, L:es Houches Lecture 2004, pdf
  • A. Jevicki, Instantons and the 1/N1/N expansion in nonlinear σ\sigma models, Phys. Rev. D 20, 3331–3335 (1979) pdf
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  • E. Brézin, S.R. Wadia, eds. The Large N Expansion in Quantum Field Theory and Statistical Physics, a book collection of reprinted historical articles, gBooks
  • Yuri Makeenko, Methods of contemporary gauge theory, Cambridge Monographs on Math. Physics, gBooks
  • M. Bershadsky, Z. Kakushadze, C. Vafa, String expansion as large N expansion of gauge theories, Nucl.Phys. B523 (1998) 59-72hep-th/9803076, doi
  • G.T. Horowitz, H. Ooguri, Spectrum of large N gauge theory from supergravity, hep-th/9802116
  • Semyon Klevtsov, Random normal matrices, Bergman kernel and projective embeddings, arxiv/1309.7333
  • wikipedia 1/N expansion

category: physics

Revised on September 30, 2013 14:57:39 by Zoran Škoda (161.53.130.104)