HEP Colloquia 2025

by Alfredo Iorio (Charles University in Prague)

Wednesday 29 Oct 2025, 14:30 → 16:00 Europe/Rome

Sala Consiliare (Department of Physics)

Gravitational anomalies of the classical Lioville theory, Virasoro algebras, Weyl-gauging and all that

In classical Liouville field theory, diffeomorphism invariance, Weyl invariance, and locality cannot hold simultaneously. This incompatibility arises from the presence of a genuine central extension in the Virasoro algebra, already at the classical level. Its consequences are twofold: in flat space, the energy-momentum tensor fails to transform conformally as a tensor and, in curved space, it acquires a non-vanishing trace.

Our analysis focuses on a field-independent term, proportional to the square of the Weyl gauge field, which restores Weyl invariance of Liouville action. This term has been often neglected in prior treatments of conformal and Weyl symmetries. It encodes the classical Virasoro center and reveals a geometric obstruction to reconciling symmetries and locality. Its presence clarifies the origin of classical anomalies and invites a reexamination of the interplay between gauge structure and conformal geometry.