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.
Asyzygies, modular forms, and the superstring measure I
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abstract
The goal of this paper and of a subsequent continuation is to find some viable ansatze for the three-loop superstring chiral measure. For this, two alternative formulas are derived for the two-loop superstring chiral measure. Unlike the original formula, both alternates admit modular covariant generalizations to higher genus. One of these two generalizations is analyzed in detail in the present paper, with the analysis of the other left to the next paper of the series.
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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.