Uniqueness of the minimum of the free energy of the 2-D Yang-Mills theory at large N

There have been some controversies about the large N behaviour of the 2-D Y ang-Mills and chiral 2-D Yang-Mills theories. To be more specific, is there a one-parameter family of minima of the free energy in the strong region, or is the minimum unique? We show that by adding an equation (which was mis sing) to the known equations, the minimum becomes unique.