  We prove a general theorem on spectral convexity with respect to particle
number for 2N degenerate components of fermions. The number of spatial
dimensions is arbitrary, and the system may be uniform or constrained by an
external potential. We assume only that the interactions are governed by an
SU(2N)-invariant two-body potential whose Fourier transform is negative
definite. The convexity result implies that the ground state is in a
2N-particle clustering phase. We discuss implications for light nuclei as well
as asymmetric nuclear matter in neutron stars.
