BRST quantization of one-dimensional gravity

The BRST Ward identities in one-dimensional gravity on a closed manifold, which is analogous to the first quantized theory of a bosonic string, are investigated. It is shown that the BRST Ward identities are anomalous, the anomaly being due to the noninvariance of the domain of the functional integration with respect to the BRST transformations. A modified non-anomalous BRST operator is introduced, and decoupling of spurions from the physical states is established.