Does a given lattice of a torus (either twisted or untwisted) admit only certain orbifolds - ie. only specific [tex]N[/tex] of [tex]Z_N[/tex] ?(adsbygoogle = window.adsbygoogle || []).push({});

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 [tex]Z_3[/tex] symmetry. But why cannot it have a [tex]Z_2[/tex] symmetry? Here, under a [tex]Z_2[/tex] orbifold, the fixed points change to [tex]z=\{0, 0.5\}[/tex] - fixed under [tex]e^{i\pi}[/tex] - right?

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# Orbifold (basics)

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