  We derive nonlinear sigma models (chiral Lagrangians) over symmetric spaces
U(n), U(2n)/Sp(2n), and U(2n)/O(2n) from U(N), O(N), and Sp(2N) lattice gauge
theories coupled to n flavors of staggered fermions, in the large-N and g^2 N
limit. To this end, we employ Zirnbauer's color-flavor transformation. We prove
the spatial homogeneity of the vacuum configurations of mesons by explicitly
solving the large-N saddle point equations, and thus establish the above
patterns of spontaneous chiral symmetry breaking without any assumptions.
