We are dealing with two-dimensional gravitational anomalies, specifically with the Einstein anomaly and the Weyl anomaly, and we show that they are fully determined by dispersion relations independent of any renormalization procedure (or ultraviolet regularization). The origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor. In the zero mass limit the imaginary part of the formfactor approaches a δ-function singularity at zero momentum squared, exhibiting in this way the infrared feature of the gravitational anomalies. We find an equivalence between the dispersive approach and the dimensional regularization procedure. The Schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method. Although all computations are performed in two dimensions the method is expected to work in higher dimensions too. * This work was partly supported by Austria-Czech Republic Scientific collaboration, project KON-TACT 1999-8. † Supported by a Wissenschaftsstipendium der Magistratsabteilung 18 der Stadt Wien.

Using a recent technique, proposed by Eardley and Giddings, we extend their results to the high-energy collision of two beams of massless particles, i.e. of two finite-front shock waves. Closed (marginally) trapped surfaces can be determined analytically in several cases even for collisions at nonvanishing impact parameter in D ≥ 4 space-time dimensions. We are able to confirm and extend earlier conjectures by Yurtsever, and to deal with arbitrary axisymmetric profiles, including an amusing case of "fractal" beams. We finally discuss some implications of our results in high-energy experiments and in cosmology.

We consider non-compact Z N orientifold models of type IIB superstring theory with four-dimensional gravity induced on a set of coincident D3-branes. For the models with odd N the contribution to the one-loop renormalization of the Planck mass is shown to come only from the torus and to be O(N ) as the contributions from annulus, Moebius strip and Klein bottle cancel. One can therefore realize the Dvali-Gabadadze-Porrati idea that four-dimensional gravity is induced by quantum effects at the one-loop level by considering large N .