Polyakov Soldering and Second-Order Frames: The Role of the Cartan Connection

2008/02/29 by Serge Lazzarini, Carina Tidei · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s11005-008-0253-8

published as Lett.Math.Phys.85:27-37,2008 · Accepté pour publication dans Lett. Math. Phys

openalex publication_date 2008/07/01 · arxiv created 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 RP¹. 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.

Cited by

• Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors