糖果派对

Speaker: Nadia Ott聽(University of Southern Denmark)


Abstract:

D鈥橦oker and Phong鈥檚 calculation of the genus g = 2 superstring amplitude uses, in a crucial way, a projection from genus g = 2 supermoduli space to its underlying reduced space. They define this projection using a formula for the genus g = 2 super period matrix. Witten generalized their formula for the super period matrix to higher genus g and found that the super period matrix may develop a pole along a particular divisor in supermoduli space if 驳听鈮� 11. This divisor is commonly called the bad divisor. Witten also considered super period matrices on super Riemann surfaces with a nonzero number of Ramond punctures (note: the word puncture is a bit of a misnomer). He found that in the presence of Ramond punctures, a closed one form has, in addition to the usual 2g 鈥漞ven鈥� periods (defined by integrals over one cycle in homology), 2r fermionic periods. The fermionic periods of one form w聽are certain constants appearing in the restriction of w聽to the Ramond divisor. In joint work with Ron Donagi, we identify the 2r fermionic periods of w with the residues of a particular global section of the twisted spin structure on the underlying curve. As in the unpunctured case, the super period matrix with Ramond punctures may develop a singularities as we vary over supermoduli space. Using this identification of the fermionic periods in terms of residues, we explicitly describe this bad locus in supermoduli space.