Quantization of the first-order two-dimensional Einstein-Hilbert action

A canonical analysis of the first-order two-dimensional Einstein-Hilbert action has shown it to have no physical degrees of freedom and to possess an unusual gauge symmetry with a symmetric field xi(mu nu) acting as a gauge function. Some consequences of this symmetry are explored. The action is quantized and it is shown that in a 'Landau gauge' all loop diagrams beyond one-loop order vanish. Furthermore, explicit calculation of the one-loop two-point function shows that it too vanishes, with the contribution of the ghost loop cancelling that of the 'graviton' loop.