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A bosonic string is a relativistic one-dimensional object whose embedding coordinates are bosonic fields on a two-dimensional worldsheet. Its classical motion can be described by the Nambu–Goto action, proportional to the worldsheet area, or by the equivalent Polyakov action with an auxiliary worldsheet metric.

An open string has endpoints; a closed string forms a loop and has independent left- and right-moving oscillations. Quantization produces a tower of particle states. In the ordinary flat critical bosonic string theory, anomaly cancellation selects 26 spacetime dimensions, and the closed-string spectrum includes a massless graviton. The tachyonic ground state indicates instability of the chosen vacuum.^[ref]

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]