The Chiral Superstring Siegel Form in Degree Two Is a Lift

Abstract

Abstract. We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t/2 over the theta group Γ 1 (1, 2) to Siegel modular cusp forms over certain subgroups Γ para (t; 1, 2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.