Free Field Realization of Cylindrically Symmetric Einstein Gravity

TL;DR

This paper demonstrates how cylindrically symmetric Einstein gravity can be reformulated as a free-field theory using canonical transformations, simplifying quantization and providing new insights into its structure.

Contribution

It introduces a canonical transformation that maps cylindrically symmetric Einstein gravity to free fields, facilitating easier quantization and analysis.

Findings

The theory can be mapped to free fields with a Minkowskian target space.

Quantization in free-field variables is significantly simpler.

The approach leverages the asymptotic behavior of the Ernst equation.

Abstract

Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$ sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation we show that the theory can be mapped by a canonical transformation into a set of free fields with a Minkowskian target space. We briefly discuss the quantization in terms of these free-field variables, which is considerably simpler than in the other approaches.