This lecture develops picture-changing operators to resolve a mismatch in superstring scattering-amplitude prescriptions: the required total background charge of the bosonized superconformal ghost field Phi is fixed by a curvature (Riemann-Roch-type) argument to 2(g-1) on a genus-g surface, but the naive vertex-operator prescription (unintegrated operators carrying e^{-Phi} charge -1, integrated operators carrying none) can only produce non-positive total charge, failing for genus greater than one. The fix defines a BRST-exact operator X = {Q_BRST, zeta(z)} (the "picture-changing operator," built from the zeta-eta-Phi bosonization of the beta-gamma ghost system) whose insertion is position-independent and which, when fused with a vertex operator, raises its "picture number" by shifting it toward positive powers of e^{Phi}, thereby supplying the additional charge needed at higher genus. This belongs to superstring perturbation theory / BRST quantization on the worldsheet, and it generalizes and unifies the fixed/unintegrated vs. moduli-integrated vertex operator prescription from the bosonic string to the superstring's additional "picture" degree of freedom.
This lecture develops picture-changing operators to resolve a mismatch in superstring scattering-amplitude prescriptions: the required total background charge of the bosonized superconformal ghost fi…