BRST operator ($Q_B$)

The BRST operator is the Grassmann-odd conserved charge that combines a gauge transformation with its ghost field. Quantum gauge consistency requires $Q_B^2=0$, and physical states are its cohomology classes.

The BRST current is the conserved worldsheet current whose contour integral is the BRST operator. For the bosonic string it is built from the reparameterization ghost and the matter and ghost stress tensors; its self-OPE is nonsingular only when the total central charge vanishes.