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Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, wediscuss the full set of proper BRST and anti-BRST transformations for a 2Ddiffeomorphism invariant theory which is described by the Lagrangian density ofa standard bosonic string. The above (anti-)BRST transformations are off-shellnilpotent and absolutely anticommuting. The latter property is valid on asubmanifold of the space of the quantum fields where the 2D version of theuniversal (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions aresatisfied. We derive the precise forms of the BRST and anti-BRST invariantLagrangian densities as well as the exact expressions for the conserved(anti-)BRST and ghost charges. The lucid derivation of the proper anti-BRSTsymmetry transformations and the emergence of the CF-type restrictions arecompletely novel results for our present bosonic string which has already beendiscussed earlier in literature where only the BRST symmetry transformationshave been pointed out. We briefly mention the derivation of the CF-typerestrictions from the modified version of Bonora-Tonin superfield approach,too.

Nilpotent Symmetries of a Model of 2D Diffeomorphism Invariant Theory: BRST Approach