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 an...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 287; no. 2; pp. 749 - 767
Main Author Grushevsky, Samuel
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.04.2009
Springer
Subjects
Algebra
Classical and Quantum Gravitation
Complex Systems
Exact sciences and technology
Mathematical and Computational Physics
Mathematical methods in physics
Mathematical Physics
Mathematics
Number theory
Other topics in mathematical methods in physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Sciences and techniques of general use
Theoretical
Modulus Space
Abelian Variety
Modular Form
High Genus
Symplectic Form
Modular form
Mathematical physics
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ISSN0010-3616
1432-0916
DOI10.1007/s00220-008-0635-x

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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-008-0635-x