  We consider the finite-volume spectra of QCD in the chiral limit of massless
up and down quarks and massive strange quarks in the baryon number sectors $B =
0$ and $B = 1$ for different values of the isospin. Spontaneous symmetry
breaking gives rise to rotor spectra, as the chiral order parameter precesses
through the vacuum manifold. Baryons of different isospin influence the motion
of the order parameter through non-trivial Berry phases and associated abstract
monopole fields. Our investigation provides detailed insights into the dynamics
of spontaneous chiral symmetry breaking in QCD on a torus. It also sheds new
light on Berry phases in the context of quantum field theory. Interestingly,
the Berry gauge field resulting from QCD solves a Yang-Mills-Chern-Simons
equation of motion on the vacuum manifold $SU(2) = S^3$.
