| Popis: |
Classical anomalies defined as due to centrally extended algebras of Noether charges are discussed. Specific emphasis is given to the (anomalous) conformal symmetry in two dimensions, governed by the Virasoro algebra of the Noether charges. Liouville field theory as an example of a classically anomalous theory is studied, in flat and curved spacetimes. We find that the presence of a central charge leads to an energy-momentum tensor with non- tensorial conformal transformations in flat spacetime and a non-vanishing trace in curved spacetime. A set of improvements of Liouville theory, leading to the Weyl invariance, is given. By explicit calculations it is shown how the conservation of the improved energy-momentum tensor is lost, while the improvements restore the tracelessness and the relation between the chosen improvement and the corresponding subset of preserved diffeomorphisms is given. The non-tensorial transformation rule of the improved energy-momen- tum tensor in a curved spacetime is related back to the central charge of the Virasoro algebra. |
