Polyakov soldering and second order frames : the role of the Cartan connection

Serge Lazzarini (1, 2) , Carina Tidei (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

The so-called "soldering" procedure performed by A.M.~Polyakov in [1] for a SL(2,R)-gauge theory is geometrically explained in terms of a Cartan connection on second order frames of the projective space RP^1. The relationship between a Cartan connection and the usual (Ehresmann) connection on a principal bundle allows to gain an appropriate insight into the derivation of the genuine " diffeomorphisms out of gauge transformations" given by Polyakov himself.

Mots clés: Higher order frames; Cartan connection; Polyakov soldering

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Serge Lazzarini, Carina Tidei. Polyakov soldering and second order frames : the role of the Cartan connection. Letters in Mathematical Physics, 2008, 85 (1), pp.27-37. ⟨10.1007/s11005-008-0253-8⟩. ⟨hal-00258919v2⟩