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
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.