We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup of the modular group. An explicit formula for this form, as a polynomial in the even theta constants, is given. We checked that our result is consistent with the vanishing of the cosmological constant. We also verified a conjecture of D'Hoker and Phong on modular forms in genus 3 and 4 using results of Igusa.
|Titolo:||Modular forms and three loop superstring amplitudes|
VAN GEEMEN, LAMBERTUS (Ultimo)
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2008|
|Digital Object Identifier (DOI):||10.1016/j.nuclphysb.2008.03.007|
|Appare nelle tipologie:||01 - Articolo su periodico|