Open string stretched between D-branes

An open string stretched a distance $L$ between parallel D-branes has squared mass $M^2=T^2{L}^2+(N-1)/{\alpha }^{\prime }$. The stretching energy makes strings between separated branes massive.

When $n$ parallel D-branes coincide, oriented strings joining distinct branes become massless alongside strings whose ends lie on one brane. Their Chan-Paton labels fill the adjoint representation of $U(n)$, enhancing $U(1{)}^n$ to $U(n)$.