  We give a topological classification of stable and unconfined massive
particles and strings (and some instantons) in worldvolume theories of
M5-branes and their dimensional reductions, generalizing Witten's
classification of strings in SYM. In particular 4d N=2 SQCD softly broken to
N=1 contains torsion (Douglas-Shenker) Z_N-strings and nontorsion (Hanany-Tong)
Z-strings. Some of the former are stable when the flavor symmetry is gauged,
while those that are not stable confine quarks and in some vacua even dyons
into baryons. The nontorsion strings are stable if and only if all colors are
locked to flavors, which is weaker than the BPS condition. As a byproduct
unstable string decay modes and approximate lifetimes are found. Cascading
theories have no vortices stabilized by the topological charges treated here
and in particular Gubser-Herzog-Klebanov axionic strings do not carry such a
charge.
