# Superstring Scattering Amplitudes in Higher Genus

@article{Grushevsky2009SuperstringSA, title={Superstring Scattering Amplitudes in Higher Genus}, author={Samuel Grushevsky}, journal={Communications in Mathematical Physics}, year={2009}, volume={287}, pages={749-767} }

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…

## 45 Citations

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We propose a procedure to determine the moduli-space integrands of loop-level superstring amplitudes for massless external states in terms of the field theory limit. We focus on the type II…

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We give a hyperelliptic formulation of the Ansatz of D’Hoker and Phong. We give an explicit family of binary invariants, one for each genus, that satisfies this hyperelliptic Ansatz. We also prove…

## References

SHOWING 1-10 OF 30 REFERENCES

Two Loop Superstring Amplitudes and S6 Representations

- Mathematics
- 2008

In this paper we describe how representation theory of groups can be used to shorten the derivation of two loop partition functions in string theory, giving an intrinsic description of modular forms…