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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**