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Riemann surface of four closed string interaction (Zwiebach section26.5)

  1. Feb 27, 2010 #1
    There are three kinds of light-cone string diagrams for four closed string interactions. As displayed by fig. 26.10, 26.11 and 26.12 of section 26.5 of Zwiebach's book.

    For each light-cone string diagram, it is characterized by two parameters, the time difference of the two interaction points, [tex]\Delta T[/tex] and the twist angle [tex]\theta[/tex].

    As for the corresponding Riemann surfaces of the three diagrams, it turns out that the three Riemann surfaces comprise a Riemann sphere with four punctures.

    The subtlety I don't understand is the resulting moduli space. It turns out to be [tex]M_{0,4}[/tex], the Riemann sphere with three punctures. The three kinds of light-cone string diagrams contribute three disks which are fully cover [tex]M_{0,4}[/tex]. What I don't understand is, for the diagram, fig. 26.10, the corresponding moduli is a deformed disk. The last paragraph of this section mentioned that "...the one around [tex]\lambda = 0[/tex] has an unusual shape. You may take it as a good challenge to explain the features of Figure 26.13 by looking carefully at the [tex]\theta[/tex] dependence of each of the three string diagrams in the limit that the intermediate time goes to zero."

    Thanks for any further or detail explanations.
     
  2. jcsd
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