Superstring scattering amplitudes in higher genus

Details Superstring scattering amplitudes in higher genus Superstring scattering amplitudes in higher genus

2008-03-24

arxiv.org/abs/0803.3469v2

Commun.Math.Phys.287:749-767,2009

Physics

High Energy Physics

High Energy Physics - Theory

Minor changes; final version to appear in Comm. Math. Phys

Scientific paper

10.1007/s00220-008-0635-x

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 ans\"atze 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.

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