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The BRST current is the conserved worldsheet current whose closed contour integral gives the BRST operator,For the bosonic string, one conventional holomorphic representative iswhere $b,c$ are the worldsheet ghost fields, $T_m$ is the matter stress-energy tensor, and colons denote normal ordering. The last term improves the conformal transformation law without changing the closed contour integral.

Quantum consistency requires $Q_B^2=0$. With matter central charge $c_m$ and ghost central charge $-26$, the obstructing contour residue vanishes at $c_m=26$. This does not require a nonsingular operator product expansion of the currents. For the displayed representative, even at $c_m=26$ the singular terms areThere is no simple pole, so the inner contour integral vanishes. The BRST operator can therefore be nilpotent while its local current has higher-order poles.^[ref]

Dan Israël developed a systematic teaching account of string theory that connects the string worldsheet with quantization and conformal field theory. His notes work from the classical string description toward the quantum consistency and interaction problems.^[ref]

The distinction between worldsheet coordinates and target-spacetime coordinates is foundational: a field on the two-dimensional worldsheet can describe how a string is embedded in a higher-dimensional spacetime. The formulation separates the model's internal description from the space in which its physical excitations are interpreted.