ar X iv : h ep - t h / 03 06 05 9 v 1 7 J un 2 00 3 Vanishing of the conformal anomaly for strings in a gravitational wave

Using the non-symmetric-connection approach proposed by Osborn, we demonstrate that, for a bosonic string in a specially chosen plane-fronted gravitational wave and an axion background, the conformal anomaly vanishes at the two-loop level. Under some conditions, the anomaly vanishes at all orders. 1. Introduction. In a recent paper [1] Osborn carried out a two-loop calculation of the β-functions of a bosonic string in the presence of a non-trivial background metric g µν and of an antisymmetric axion field b µν. He used dimensional regularization, extending the two-dimensional antisymmetric tensor ǫ στ into a complex structure in 2n dimensions. An immediate consequence of his procedure was to combine the metric and the axion into a single, non-symmetric tensor t µν ; the three-form H µνρ associated to the axion appears as the torsion of the non-symmetric connection. In this Letter we apply Osborn's conceptual framework to an explicit example, namely to string propagation in a generalized pp wave (plane-fronted gravitational wave with parallel rays) of the type discussed by Brinkmann [2], whose metric is