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Hi,
recently I'm studying some stuff about T-duality in string theory, toroidal compactification and doubled geometry. Now I think I understand the moduli space of a torus, [itex]T^2[/itex], but apparently (see for instance Hull's "Doubled geometry and T-folds") one can write the moduli [itex]\tau[/itex] of [itex]T^d[/itex] as elements of
[tex]
\tau \in \frac{O(d,d)}{O(d)\times O(d)}
[/tex]
So my question is, is there an intuitive way to see that the moduli space of [itex]T^d[/itex] is
[itex]\frac{O(d,d)}{O(d)\times O(d)}[/itex]? Can I see those O(d)'s as acting on the cycles of the tori or something like that? Where does this O(d,d) come from? Thanks in forward!
recently I'm studying some stuff about T-duality in string theory, toroidal compactification and doubled geometry. Now I think I understand the moduli space of a torus, [itex]T^2[/itex], but apparently (see for instance Hull's "Doubled geometry and T-folds") one can write the moduli [itex]\tau[/itex] of [itex]T^d[/itex] as elements of
[tex]
\tau \in \frac{O(d,d)}{O(d)\times O(d)}
[/tex]
So my question is, is there an intuitive way to see that the moduli space of [itex]T^d[/itex] is
[itex]\frac{O(d,d)}{O(d)\times O(d)}[/itex]? Can I see those O(d)'s as acting on the cycles of the tori or something like that? Where does this O(d,d) come from? Thanks in forward!