Chiral-Symmetry Breakdown in Large-NChromodynamics

Chromodynamics with $n$ flavors of massless quarks is invariant under chiral $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}\otimes \mathrm{U}\mathrm{}\left(n\right)\mathrm{}$. It is shown that in the limit of a large number of colors, under reasonable assumptions, this symmetry group must spontaneously break down to diagonal $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}$.