Remarks on superstring amplitudes in higher genus. (English) Zbl 1189.81182
Summary: Very recently, Grushevsky continued D’Hoker and Phong’s program of finding the chiral superstring measure from first principles by constructing modular forms satisfying certain factorization constraints. He has proposed an ansatz in genus 4 and conjectured a possible formula for the superstring measure in any genus, subject to the condition that certain modular forms admit holomorphic roots. In this note we want to give some evidence that Grushevsky’s approach seems to be very fruitful.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
| 11Z05 | Miscellaneous applications of number theory |
| 14H15 | Families, moduli of curves (analytic) |
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