Asyzygies, modular forms, and the superstring measure II

Details Asyzygies, modular forms, and the superstring measure II Asyzygies, modular forms, and the superstring measure II

2004-11-19

arxiv.org/abs/hep-th/0411182v1

Nucl.Phys. B710 (2005) 83-116

Physics

High Energy Physics

High Energy Physics - Theory

41 pages

Scientific paper

10.1016/j.nuclphysb.2004.12.020

Precise factorization constraints are formulated for the three-loop superstring chiral measure, in the separating degeneration limit. Several natural Ans\"atze in terms of polynomials in theta constants for the density of the measure are examined. None of these Ans\"atze turns out to satisfy the dual criteria of modular covariance of weight 6, and of tending to the desired degeneration limit. However, an Ansatz is found which does satisfy these criteria for the square of the density of the measure, raising the possibility that it is not the density of the measure, but its square which is a polynomial in theta constants. A key notion is that of totally asyzygous sextets of spin structures. It is argued that the Ansatz produces a vanishing cosmological constant.

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