2-DIMENSIONAL QCD WITH MATTER IN THE ADJOINT REPRESENTATION - WHAT DOES IT TEACH US

Citation
Ii. Kogan et Ar. Zhitnitsky, 2-DIMENSIONAL QCD WITH MATTER IN THE ADJOINT REPRESENTATION - WHAT DOES IT TEACH US, Nuclear physics. B, 465(1-2), 1996, pp. 99-116
Citations number
46
Categorie Soggetti
Physics, Nuclear
Journal title
ISSN journal
05503213
Volume
465
Issue
1-2
Year of publication
1996
Pages
99 - 116
Database
ISI
SICI code
0550-3213(1996)465:1-2<99:2QWMIT>2.0.ZU;2-G
Abstract
We analyse the highly excited states in QCD(2)(N-c --> infinity) with adjoint matter by using such general methods as dispersion relations, duality and unitarity. We find the Hagedorn-like spectrum rho(m) simil ar to m(-a) exp(beta(H)m) where the parameters beta H and a can be exp ressed in terms of the asymptotics of the matrix elements f(n{k}) simi lar to [O\Tr(<(Psi)over bar>Psi)(k)\n(k)]. We argue that the asymptoti cal values f(n{k}) do not depend on k (after appropriate normalization ). Thus, we obtain beta(H) = (2/pi)root pi/g(2)N(c) and a = -3/2 in th e case of Majorana fermions in the adjoint representation. The Hagedor n temperature is the limiting temperature in this case. We also argue that the chiral condensate [O\Tr(<(Psi)over bar>Psi)\O] is not zero in the model. Contrary to the 't Hooft model, this condensate does not b reak down any continuous symmetries and can not be considered as an or der parameter. Thus, no Goldstone boson appears as a consequence of th e condensation. We also discuss a few apparently different but actuall y tightly related problems: master field, condensate, wee partons and constituent quark model in the light-cone framework.