The magnon kinematics of the AdS/CFT correspondence

TL;DR

This paper explores the integrable structure of planar N=4 supersymmetric Yang-Mills theory, focusing on magnon kinematics, Hopf algebra symmetries, and their implications for the spectrum and dispersion relations.

Contribution

It identifies the role of an abelian Hopf algebra in describing magnon length fluctuations and derives constraints on magnon irreps and dispersion relations.

Findings

Magnon dispersion relation derived from Hopf algebra constraints

Crossing symmetry analyzed within the Z symmetry spectrum

Discussion of giant magnon semiclassical regime

Abstract

The planar dilatation operator of N=4 supersymmetric Yang-Mills is the hamiltonian of an integrable spin chain whose length is allowed to fluctuate. We will identify the dynamics of length fluctuations of planar N=4 Yang-Mills with the existence of an abelian Hopf algebra Z symmetry with non-trivial co-multiplication and antipode. The intertwiner conditions for this Hopf algebra will restrict the allowed magnon irreps to those leading to the magnon dispersion relation. We will discuss magnon kinematics and crossing symmetry on the spectrum of Z. We also consider general features of the underlying Hopf algebra with Z as central Hopf subalgebra, and discuss the giant magnon semiclassical regime.