The Asymptotic Spectrum of the N=4 Super Yang-Mills Spin Chain

TL;DR

This paper analyzes the asymptotic spectrum of the N=4 Super Yang-Mills spin chain, revealing the structure of states and deriving exact dispersion relations using group theory.

Contribution

It extends Beisert's analysis to bound states, providing a group-theoretic derivation of the dispersion relation for all magnon bound states.

Findings

Spectrum characterized by SU(2|2) x SU(2|2) representations

Bound states form short representations of dimension 16Q^2

Exact dispersion relations derived for all bound states

Abstract

In this paper we discuss the asymptotic spectrum of the spin chain description of planar N=4 SUSY Yang-Mills. The states appearing in the spectrum belong to irreducible representations of the unbroken supersymmetry SU(2|2) x SU(2|2) with non-trivial extra central extensions. The elementary magnon corresponds to the bifundamental representation while boundstates of Q magnons form a certain short representation of dimension 16Q^{2}. Generalising the Beisert's analysis of the Q=1 case, we derive the exact dispersion relation for these states by purely group theoretic means.