Large–N limit of the generalized 2D Yang–Mills theory on cylinder

Using the collective field theory approach of large–N generalized two–dimensional Yang–Mills theory on cylinder, it is shown that the classical equation of motion of collective field is a generalized Hopf equation. Then, using the Itzykson–Zuber integral at the large–N limit, it is found that the classical Young tableau density, which satisfies the saddle–point equation and determines the large–N limit of free energy, is the inverse of the solution of this generalized Hopf equation, at a certain point. PACS nubers: 11.10.Kk, 11.15.Pg, 11.15.Tk Kewwords: large–N , Yang–Mills theory, generalized Hopf equation, density function e-mail:[email protected] e-mail:[email protected]