A First Course in String Theory

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2.5 Constructing orbifold

(a) A fundamental domain, with its boundary, is the parallelogram with corners at and . Where is the fourth corner? Make a sketch and indicate the identifications on the boundary. The resulting space is an oblique torus.

(b) Consider now an *additional* identification

To understand how this identification acts on the oblique torus, draw the short diagonal that divides the torus into two equilateral triangles. Describe carefully the action on each of the two triangles (recall that the action of can be followed by arbitrary action with , , and their inverses).

[guess]

(a)

(b)

[guess]

— Me@2021-02-11 06:03:36 PM

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2021.02.12 Friday (c) All rights reserved by ACHK

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