Two-dimensional QCD with matter in the adjoint representation: What does it teach us? Original Research Article

We analyse the highly excited states in QCD2(Nc → ∞) with adjoint matter by using such general methods as dispersion relations, duality and unitarity. We find the Hagedorn-like spectrum ϱ(m) ∼ m−a exp(βHm) where the parameters βH and a can be expressed in terms of the asymptotics of the matrix elements fnk ∼ 〈0|Tr(Ψ−Ψ)k|nk〉. We argue that the asymptotical values fnk do not depend on k (after appropriate normalization). Thus, we obtain βH = (2π)√πg2Nc and a = −32 in the case of Majorana fermions in the adjoint representation. The Hagedorn temperature is the limiting temperature in this case.