T-duality II - Open Strings

Now, we will consider compactification $x^d\sim x^d+2\pi R$ and T-duality for open strings. At first glance, there is nothing surprising because for open strings with Neumann boundary conditions, there is a number comparable to the winding number. There is no new continuum of states as $R\to 0$ and the behaviour is akin to field theory; the remaining states have momentum only in $d=D-1$ dimensions.

However, the interior of an open string is identical to the interior of a closed string and therefore should be moving in $D$ dimensions far from the end-points by T-duality. The end-points must be restricted to move in a $d$-dimensional hyperplane in the T-dual picture. This hyperplane is known as a D-brane.

• Action of T-duality
• Chan-Paton Factors
• Wilson Lines
• Multiple D-branes