Quark-mass dependence of gluonic boundary conditions

Quark condensation with (n2-1) small-mass bosons requires the topological charge spectrum [ν] to depend on ratios of the quark masses which explicitly violate chiral SU(n) x SU(n) symmetry. General conditions are derived for non-integer ν and hence two vacua at theta = π (mod 2π), and for [ν] to be quantized in rational units. The results show that gluonic boundary conditions are influenced by quark dynamics. (orig.)