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This is driving me nuts. Hope someone can explain this to me.
To classify conformally inequivalent tori, one introduces the parameter tau. Tori with tau =tau +1 and tau = -1/tau are conformally equivalent.
Now, consider two conformally inequivalent tori. Let's say one has tau =i and the other one has tau = i +1/2.
Zwiebach calls the first one a "rectangular torus".
How can we visualize the torus with tau = i+1/2 ?
Zwiebach draws a picture in figure 23.18 but I don't get it.The figure indicates that if we move along one cycle of a torus, we end up shifted a certain amount in the perpendicular direction. I don't understand how we can not, for any torus, simply go along a cycle and get back to the same position. That seems trivially possible for any torus!
Hope someone can clarify this.
Thanks
To classify conformally inequivalent tori, one introduces the parameter tau. Tori with tau =tau +1 and tau = -1/tau are conformally equivalent.
Now, consider two conformally inequivalent tori. Let's say one has tau =i and the other one has tau = i +1/2.
Zwiebach calls the first one a "rectangular torus".
How can we visualize the torus with tau = i+1/2 ?
Zwiebach draws a picture in figure 23.18 but I don't get it.The figure indicates that if we move along one cycle of a torus, we end up shifted a certain amount in the perpendicular direction. I don't understand how we can not, for any torus, simply go along a cycle and get back to the same position. That seems trivially possible for any torus!
Hope someone can clarify this.
Thanks