Strings Inside Walls in N=1 Super Yang-Mills

We conjecture the existence of strings bounded inside walls in SU$(n)$ $\mathbb{N}=1$ Super Yang-Mills theory. These strings carry ${\mathbb{Z}}_{[k,n]}$ quantum number, where $[k,n]$ is the greatest common divisor between $k$, the charge of the wall, and $n$. We provide field-theoretical arguments and string-theoretical evidences, both from MQCD and from gauge-gravity correspondence. We interpret this result from the point of view of the low-energy effective action living on the $k$-wall.