An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry

TL;DR

This paper explores the algebraic origins of the Yangian symmetry in the AdS/CFT spin chain, revealing a connection to the exceptional superalgebra d(2,1;epsilon) and its epsilon-correction.

Contribution

It demonstrates that the Yangian symmetry in the AdS/CFT spin chain can be derived from the exceptional superalgebra d(2,1;epsilon), providing new insights into its algebraic structure.

Findings

Rederived Yangian symmetries using the exceptional superalgebra.

Identified epsilon-correction as the source of the novel symmetry.

Reproduced the non-canonical classical r-matrix from the exceptional algebra.

Abstract

In the su(2|2) spin chain motivated by the AdS/CFT correspondence, a novel symmetry extending the superalgebra su(2|2) into u(2|2) was found. We pursue the origin of this symmetry in the exceptional superalgebra d(2,1;epsilon), which recovers su(2|2) when the parameter epsilon is taken to zero. Especially, we rederive the Yangian symmetries of the AdS/CFT spin chain using the exceptional superalgebra and find that the epsilon-correction corresponds to the novel symmetry. Also, we reproduce the non-canonical classical r-matrix of the AdS/CFT spin chain expressed with this symmetry from the canonical one of the exceptional algebra.