# Orbifold (basics)

1. Dec 30, 2009

### crackjack

Does a given lattice of a torus (either twisted or untwisted) admit only certain orbifolds - ie. only specific $$N$$ of $$Z_N$$ ?

For example, consider the twisted torus lattice (in complex plane) in page 121 of Green, Schwarz & Witten 's Vol-2 book. It is said (in page 122) that the torus is special, in that, it has a $$Z_3$$ symmetry. But why cannot it have a $$Z_2$$ symmetry? Here, under a $$Z_2$$ orbifold, the fixed points change to $$z=\{0, 0.5\}$$ - fixed under $$e^{i\pi}$$ - right?

Last edited: Dec 31, 2009