More on superstring chiral measures

Abstract

In this paper we study the expressions of the superstring chiral measures for $g\le 5$. We obtain certain new expressions which are functions of higher powers of theta constants. For $g=3$ we show that the measures can be written in terms of fourth power of theta constants and for $g=4$ in terms of squares of theta constants. In both cases the forms ${\Xi }_8^{(g)}[0^{(g)}]$ appearing in the expression of the measures are defined on the whole Siegel upper half space. Instead, for $g=5$ we find a form ${\Xi }_8^{(5)}[0^{(5)}]$ which is a polynomial in the classical theta constants, well defined on the Siegel upper half space and satisfying some suitable constraints on the moduli space of curves (and not on the whole Siegel upper half space) that could be a candidate for the genus five superstring measure. Moreover, we discuss the problem of the uniqueness of this form in genus five. We also determine the dimension of certain spaces of modular forms and reinterpret the vanishing of the cosmological constant in terms of group representations.

36 pages

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Cited by in corpus (7)

• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• Classical theta constants vs. lattice theta series, and super string partition functions
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• The superstring cosmological constant and the Schottky form in genus 5
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Finite Strings From Non-Chiral Mumford Forms
• Singular Spin Structures and Superstrings