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Superstring Scattering Amplitudes in Higher Genus

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Abstract

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.

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Authors and Affiliations

  1. Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544, USA

    Samuel Grushevsky

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  1. Samuel Grushevsky
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Correspondence to Samuel Grushevsky.

Additional information

Communicated by A. Kapustin

Research is supported in part by National Science Foundation under the grant DMS-05-55867.

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Grushevsky, S. Superstring Scattering Amplitudes in Higher Genus. Commun. Math. Phys. 287, 749–767 (2009). https://doi.org/10.1007/s00220-008-0635-x

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  • DOI: https://doi.org/10.1007/s00220-008-0635-x

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