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Séminaires Interactions Fondamentales

Séminaire organisé par les quatre équipes du groupe Interactions fondamentales.

Responsable : Federico Piazza
Jour dédié : le vendredi à 14h00
Lieu : CPT, amphithéâtre du 5ème étage
Abonnement iCal, Séminaires passés

Prochain Séminaires Interactions Fondamentales

Vendredi 24 novembre

11h00 – 12h00, Amphi 5 du CPT

On the regularization of BF theory

Philippe Mathieu (LAPTH, Université de Savoie)

The so-called Ponzano-Regge model is an attempt to define a quantum theory of gravity. Using the formalism of tetrades, the partition function of such a theory can be written in terms of a SU(2) BF action then can be reduced to a sum over the representations of SU(2) which is thus ill-defined. This is regularized replacing the representations of SU(2) by a period of periodic representations of Uq(SU(2)). This regularization is ad hoc since until then no one has been able to deal properly with path integral. The result is then written under the form of Turaev-Viro topological invariant.

We will see that, in the case of abelian BF theory, however, thanks to Deligne-Beilinson cohomology, we can clearly identify the degrees of freedom of the theory and extract the relevant toplogical information. The regularization appearing is then natural and is related to an abelian version of Turaev-Viro invariant in a way analogous to the so-called Deloup-Turaev reciprocity formula that connects abelian Chern-Simons theory on the one hand and an abelian version of Reshetikhin-Turaev invariant on the other hand.