The chiral superstring Siegel form in degree two is a lift

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 Γ1(1,2) to Siegel modular cusp forms over certain subgroups Γpara(t;1,2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift