  We discuss generalized Dirac strings associated with a given Lie group. They
live in r-dimensional complex space (r being the rank of the group). Such
strings show up in the effective Born-Oppenheimer Hamiltonian for 3d
supersymmetric Yang-Mills-Chern-Simons theories, brought up by the gluon loops.
We calculate accurately the number of the vacuum states in the effective
Hamiltonian associated with these strings. We also show that these states are
irrelevant for the final SYMCS vacuum counting. The Witten index of SYMCS
theories depends thus only on the strings generated by fermion loops and
carrying fractional generalized fluxes.
