This lecture develops the GSO (Gliozzi-Scherk-Olive) projection for the superstring by defining the fermion-number operator (-1)^F on both the Neveu-Schwarz (NS) and Ramond (R) sectors — extending the definition through the bosonized worldsheet fermions and the beta-gamma ghost system so that it commutes with the BRST charge — and then using mutual locality (single-valuedness of operator products under a 2π rotation) together with modular invariance (existence of at least one Ramond sector on each chirality) to classify which combinations of NS±/R± sectors can consistently coexist in a tachyon-free superstring theory. This belongs to the formal (covariant/BRST) construction of superstring theory, specifically the sector/spin-structure classification that precedes and motivates the GSO projection, and it is a prerequisite to defining the Type IIA and Type IIB superstring theories.
This lecture develops the GSO (Gliozzi-Scherk-Olive) projection for the superstring by defining the fermion-number operator (-1)^F on both the Neveu-Schwarz (NS) and Ramond (R) sectors — extending th…