T-duality in string theory relates a world containing open and closed strings with a D$p$-brane with a compact dimension with radius $R$ with a dual world with a D$(p-1)$-brane with a radius $R'=\alpha'/R$, where the D$(p-1)$-brane is located at an certain angle $\theta$ on the dual circle.

If you apply the duality a second time on the dual world containing a D$(p-1)$ (and imagine this brane has still a compact dimension), you get a dual dual world with a D$(p-2)$.

I'm wondering about two issues:

By duality I understand an isomorphism relating two different worlds. In the case that all $p$ dimensions of the brane are compact. Is this world containing than isomorphic to one with a D$0$-brane?

I also suppose that my understanding of a duality as an isomorphic is somehow wrong: if you apply the 'duality-map' you do not get the original D$p$-brane but a D$(p-2)$-brane.

This post imported from StackExchange Physics at 2014-08-10 13:48 (UCT), posted by SE-user Anne O'Nyme