On the Yangian Y(e_8) quantum symmetry of maximal supergravity in two dimensions

TL;DR

This paper develops an algebraic framework for quantizing the classical charge algebra of maximal supergravity in two dimensions, focusing on the Yangian Y(e_8) and its quantum deformation, to move towards an exact quantum description.

Contribution

It introduces a quantum algebraic structure based on the Yangian Y(e_8) and its twisted double, providing a foundation for the exact quantization of two-dimensional supergravity.

Findings

Identifies a unique central charge value allowing classical limit recovery.

Constructs the quantum algebra as a centrally extended twisted Yangian double.

Establishes the algebraic foundation for future exact quantization efforts.

Abstract

We present the algebraic framework for the quantization of the classical bosonic charge algebra of maximally extended (N=16) supergravity in two dimensions, thereby taking the first steps towards an exact quantization of this model. At the core of our construction is the Yangian algebra $Y(e_8)$ whose RTT presentation we discuss in detail. The full symmetry algebra is a centrally extended twisted version of the Yangian double $DY(e_8)_c$. We show that there exists only one special value of the central charge for which the quantum algebra admits an ideal by which the algebra can be divided so as to consistently reproduce the classical coset structure $E_{8(8)}/SO(16)$ in the limit $\hbar\to 0$.