In string-net theory, the density of the (oriented) string is a vector field $\vec E$. If string are all closed strings with no end, then $\vec \partial \cdot \vec E =0$. So the ends of the string are the source of $\vec E$, and correspond to the charge. The ends of strings are always discrete, impying that the charge is quantized. i.e. one end = charge-1.