Why are open strings vectors or scalars, or massive?

[Maurice7510]

In string theory, if we have NN BCs along $X^i, i = 1, \ldots, n-1$
and DD BCs along $X^a, a = n, \ldots, 25$ then you get, from $\alpha^{i,a}_{-1}|0,p\rangle$, $n$ massless vectors and $24-n$ massless scalars. I understand that for the first excited level, $M^2=0$ and so we have no mass, but what suggests that these are scalars or vectors? In the case where we have two branes separated by a distance $\delta$, with find $M^2\propto\delta^2$ which, in addition to the vector/scalar nature of the excitations, I don't understand.

 

[haushofer]

Their tensorial nature is determined by the index of the creation operator, no?

 

[Maurice7510]

I'm not sure how that would be the case though; the indices on the creation operator are $i$ (or $a$) and $-1$. The lower index is the state number (i.e. $\alpha_{-1}$ creates a one particle state) and the upper indicates indicate whether the BCs are NN or DD.