large N limit

In theoretical physics, one often considers gauge theory models whose symmetries are groups of large matrices, e.g. $U(N)$ or $O(N)$. The limit of such theories for $N\to \infty$ 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 $N$. 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 $1/N$ whose square has a simialr role to Planck constant in semiclassical approximation limit of quantum mechanics.

- A. A. Migdal,
*Loop equations and 1/N expansion*, Physics Reports, 102 (4), 199-290 (1983) doi - 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 $1/N$ expansion in nonlinear $\sigma$ models*, Phys. Rev. D 20, 3331–3335 (1979) pdf - Juan M. Maldacena,
*The large N limit of superconformal field theories and supergravity*, Adv.Theor.Math.Phys.2:231-252, 1998 hep-th/9711200;*Wilson loops in large N field theories*, hep-th/9803002. - 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)