Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude

Details Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude

2002-12-18

arxiv.org/abs/hep-th/0212219v2

Nucl.Phys. B663 (2003) 95-122

Physics

High Energy Physics

High Energy Physics - Theory

v1, LaTex file, 33 pages; v2, 34 pages, add references and minor corrections

Scientific paper

10.1016/S0550-3213(03)00381-X

We compute explicitly the four-particle amplitude in superstring theories by using the hyperelliptic language and the newly obtained chiral measure of D'Hoker and Phong. Although the algebra of the intermediate steps is a little bit involved, we obtain a quite simple expression for the four-particle amplitude. As expected, the integrand is independent of all the insertion points. As an application of the obtained result, we show that the perturbative correction to the $R^4$ term in type II superstring theories is vanishing point-wise in (even) moduli space at two loops.

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