The superstring cosmological constant and the Schottky form in genus 5

Understand

Combining certain identities for modular forms due to Igusa with Schottky-Jung relations, we study the cosmological constant for the recently proposed ansatz for the chiral superstring measure in genus 5.

• The vanishing of this cosmological constant turns out to be equivalent to the long-conjectured vanishing of a certain explicit modular form of genus 5 on the moduli of curves M_5, and we disprove this conjecture, thus showing that the cosmological constant for the proposed ansatz does not vanish identically.
• We exhibit an easy modification of the genus 5 ansatz satisfying factorization constraints and yielding a vanishing cosmological constant.
• We also give an expression for the cosmological constant for the proposed ansatz that should hold for any genus if certain generalized Schottky-Jung identities hold.