Genus four superstring measures

Cacciatori, Sergio L.; Piazza, Francesco Dalla; van Geemen, Bert

Genus four superstring measures

Authors

Cacciatori, Sergio L.

Piazza, Francesco Dalla

van Geemen, Bert

Description

A main issue in superstring theory are the superstring measures. D'Hoker and Phong showed that for genus two these reduce to measures on the moduli space of curves which are determined by modular forms of weight eight and the bosonic measure. They also suggested a generalisation to higher genus. We showed that their approach works, with a minor modification, in genus three and we announced a positive result also in genus four. Here we give the modular form in genus four explicitly. Recently S. Grushevsky published this result as part of a more general approach.
7 pages. To appear in Letters in Mathematical Physics