The asymptotic spectrum of the Script N = 4 super-Yang-Mills spin chain

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) × 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.

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

“…Since [29] reproduces the correct classical r-matrix on the fundamental representation, it would be interesting to find out if their proposal and ours are equivalent. For instance, one might compare the two when acting on bound states [52][53][54][55]11]. Whether or not they are equivalent, we believe that our approach is more suitable to find the quantisation of the bialgebra to a double Yangian Hopf algebra.…”

Geometry and topology of bubble solutions from gauge theory

“…Short representations of the symmetry group extended to P SU (2|2) × P SU (2|2) ⋉ R 3 give exact dispersion relations for elementary magnon excitations in the spin chain [22] as well as their bound states [23]. Open string solutions stretched between two points on the disc edge are interpreted as giant magnons [24] and magnon bound states [25], where the length of the string is related to the momentum carried by the magnon excitation.…”

“…, z , is a zero eigenvalue eigenstate and therefore the ground state of (24). Being the total occupation number conserved, this means a fixed total number of Zs in the excitation (23), it is possible to choose the Hamiltonian eigenstates to have definite total occupation number. We call this conserved number J.…”

Dressing phases ofAdS3/CFT2

“…A two-particle bound state will therefore transform in a representation which has the same form as the fundamental representation, differing only in the values of the central charges. This should be contrasted with the centrally extended psu(2|2) algebra appearing in AdS 5 ×S 5 [47], where the fundamental representation has dimension four while the M -particle bound state has dimension 4M [48].…”