Chiral-Symmetry Breakdown in Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>Chromodynamics

Chromodynamics with $n$ flavors of massless quarks is invariant under chiral $\mathrm{U}(n)\ensuremath{\bigotimes}\mathrm{U}(n)$. 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 $\mathrm{U}(n)$.