In Becker's book String Theory and MTheory in the chapter about Tduality and Dbrane (Chapter 6) the following comment is made
The Chan–Paton factors associate $N$ degrees of freedom with each of the end points of the string. For the case of oriented open strings, which is the case we have discussed so far, the two ends of the string are distinguished, and so it makes sense to associate the fundamental representation $N$ with the $\sigma = 0$ end and the antifundamental representation $N$ with the $\sigma =\pi$ end, as indicated in Fig. 6.3. In this way one describes the gauge group $U(N)$.

How do you know it is $U(N)$? Ok you have $N$ possibilities for the ChanPaton of each end, but why not the fundamental of $O(N)$ for example that also acts on $N$dim vectors?

I'm also confused about what the representation acts on: these are vectors with $N$ entries Do I have to picture an end as represented by a vector with a nonzero entry that 'labels' the DBrane where it is connected? And that a $U(N)$ matrix gives the result of 'some interaction' where the end shifts to another DBrane on the coincident stack.

How can you label consistently $N$ Dbranes lying at the same location? Does this actually makes sense? I mean these Dbranes fluctuate due to the massless scalar excitations. How can you disentangle them?
This post imported from StackExchange Physics at 20141011 09:51 (UTC), posted by SEuser Anne O'Nyme