The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure

TL;DR

This paper explores the algebraic structure of AdS/CFT in the strong-coupling limit, proposing a classical r-matrix with deformed symmetry that underpins a Lie bialgebra, connecting to quantum R-matrix limits.

Contribution

It introduces a classical r-matrix with deformed u(2|2) symmetry, revealing a quasi-triangular Lie bialgebra structure in AdS/CFT.

Findings

r-matrix coincides with classical limit of quantum R-matrix

establishes Lie bialgebra structure for AdS/CFT symmetry

proposes explicit algebraic expression for the r-matrix

Abstract

In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as the underlying symmetry algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.