Yangian Symmetry in Integrable Quantum Gravity

TL;DR

This paper explores the emergence of Yangian symmetry in integrable models derived from gravity theories reduced to two dimensions, revealing algebraic structures that underpin conserved charges and their quantization.

Contribution

It demonstrates how the classical Geroch group relates to a Yangian algebra and introduces a quantized twisted Yangian double with a fixed central extension.

Findings

Poisson algebra of transition matrices forms a semi-classical Yangian double with a twist.

Classical Geroch group generated by Lie-Poisson action of conserved charges.

Canonical quantization yields a twisted Yangian double with a fixed central extension.

Abstract

Dimensional reduction of various gravity and supergravity models leads to effectively two-dimensional field theories described by gravity coupled G/H coset space sigma-models. The transition matrices of the associated linear system provide a complete set of conserved charges. Their Poisson algebra is a semi-classical Yangian double modified by a twist which is a remnant of the underlying coset structure. The classical Geroch group is generated by the Lie-Poisson action of these charges. Canonical quantization of the structure leads to a twisted Yangian double with fixed central extension at a critical level.