Regularization of two-dimensional quantum gravity

The gauge sector of two-dimensional quantum gravity, which plays a central role in string theory, cannot be regularized consistently by means of the usual dimensional-regularization method. As alternatives, dimensional reduction, a variant of dimensional regularization introduced in the context of supersymmetry, and zeta-function regularization are considered. Apart from the appearance of the conformal anomaly, dimensional reduction is found to violate also two-dimensional general covariance, whereas zeta-function regularization turns out to be symmetry preserving