Communications in Mathematical Physics

, Volume 287, Issue 2, pp 749–767 | Cite as

Superstring Scattering Amplitudes in Higher Genus



In this paper we continue the program pioneered by D’Hoker and Phong, and recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the chiral superstring measure by constructing modular forms satisfying certain factorization constraints. We give new expressions for their proposed ansätze in genera 2 and 3, respectively, which admit a straightforward generalization. We then propose an ansatz in genus 4 and verify that it satisfies the factorization constraints and gives a vanishing cosmological constant. We further conjecture a possible formula for the superstring amplitudes in any genus, subject to the condition that certain modular forms admit holomorphic roots.


Modulus Space Modular Form High Genus Symplectic Form Abelian Variety 


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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA

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