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Remarks on Superstring amplitudes in higher genus
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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.
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Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT
Known one- and two-loop superstring chiral measures are restated as path integrals of the Gelca-Hamilton 3D TQFT over handlebodies, with modular transformations interpreted as bulk mapping class group moves.
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