Polyakov soldering and second order frames : the role of the Cartan connection
Serge Lazzarini (CPT), Carina Tidei (CPT)
TL;DR
This paper explains Polyakov's soldering procedure using Cartan connections on second order frames, providing geometric insights into the relationship between gauge transformations and diffeomorphisms in SL(2,R) gauge theory.
Contribution
It offers a geometric interpretation of Polyakov's soldering via Cartan connections, linking gauge theory with second order frame geometry.
Findings
Clarifies the geometric meaning of Polyakov's soldering
Connects Cartan connections with gauge and diffeomorphism transformations
Provides a new perspective on gauge theories in geometric terms
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 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.
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