# Homework Help: T-duality symmetries, how to count them?

1. May 4, 2010

### benbenny

Im reading about T-duality in string theory and im trying to understand: in a D dimensional, toroidally, compactified space, is there a symmetry for every compact dimension with itself and with every other compact dimension as well?
So, I know that T-Duality implies symmetry under
$$R^i \rightarrow \frac{\alpha'}{R^i}$$, for every dimension with itself.
But does it also imply that there is a symmetry under this change between different dimension such as:
$$R^1 \rightarrow \frac{\alpha'}{R^2}$$ and vice versa?
Im trying to count the number of such symmetries in some D dimensional space.

Thanks,

Ben