|
|
Classical anomalies
Haman, Pavel ; Iorio, Alfredo (advisor) ; Jizba, Petr (referee)
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.
|
|
|
Weyl and Conformal Symmetries
Haman, Pavel ; Iorio, Alfredo (advisor) ; Scholtz, Martin (referee)
The problem whether scale invariance implies full conformal invariance, for special relativistic classical field theories, was resolved in the literature by exploiting the Weyl and diffeomorphic symmetries held simultaneously by the suitably improved corresponding theories. In a recent study it was conjectured that, for Liouville field theory, the case is different, as such theory could not have both symmetries (Weyl and diffeomorphic) at once. In this thesis we investigate that conjecture. In the first part the conformal symmetry, and the associated Witt and Virasoro algebras, are revised. Next, we review the relationship between scale and conformal invariance, using the approach of Weyl and Ricci gauging. The last part is devoted to the Liouville field theory. We prove there the incompatibility of Weyl and diffeomorphic invariance, by showing that the particular choice of the Weyl potential, necessary to have traceless energy-momentum tensor, gives rise to an action that is not a scalar under diffeomorphisms. A preliminary study of this "classical gravitational anomaly" is also performed.
|
guest ::
