On the structure of the QCD vacuum in the large-N limit

We present an approximate QCD vacuum for SU(N → ∞). It is a generalization of the ferromagnetic vacuum first obtained by Savvidy for SU(2) and generalized by one of us to SU(3) and SU(4). Problems occuring for N ? 5 are handled in the large-Nlimit by a contnious formalism, and the vacuum obtained is characterized by N ? 1 constant, commuting, color magnetic fields with an isotropic distribution of spatial directions. The energy density of this vacuum is lower than of the perturbative vacuum by a number proportional to N², as expected from general large-N arguments. Like the Savvidy vacuum the large-N vacuum may decay into a variant of the domained Copenhagen vacuum. We give a lower limit on the domain size.