A Relativistic Relative of the Magnon S-Matrix

Abstract

We construct a relativistic scattering theory based on a q deformation and large string tension limit of the magnon S-matrix of the string world sheet theory in AdS_5 x S^5. The S-matrix falls naturally into a previously studied class associated to affine quantum groups, in this case for a twisted affine loop superalgebra associated to an outer automorphism of sl(2|2). This infinite algebra includes the celebrated triply extended psl(2|2) x R^3 algebra, but only two of the centres, the lightcone components of the 2-momentum, are non-vanishing. The algebra has the interpretation as an extended supersymmetry algebra including a non-trivial R-symmetry. The representation theory of this algebra has some complications in that tensor products are reducible but indecomposable, however, we find that structure meshes perfectly with the bootstrap, or fusion, equations of S-matrix theory. The bootstrap equations can then be used inductively to generate the complete S-matrix. Unlike the magnon theory, the relativistic theory only has a finite set of states and we find that - at least when the deformation parameter q is a root of unity - the spectrum matches precisely the soliton spectrum of the relativistic theory underlying the Pohlmeyer reduction of the string world sheet theory known as the semi-symmetric space sine-Gordon theory.

42 pages, some important typos corrected

References in corpus (20)

• Giant Magnons
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Quantum Deformations of the One-Dimensional Hubbard Model
• The S-matrix of String Bound States
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• On the Scattering of Magnon Boundstates
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Cited by in corpus (26)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On deformations of AdS_n x S^n supercosets
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Integrability of the AdS_5 x S^5 superstring and its deformations
• The Quantum Deformed Mirror TBA I
• The Quantum Deformed Mirror TBA II
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• The Bound State S-matrix of the Deformed Hubbard Chain
• Integrable Lambda Models And Chern-Simons Theories
• Exploring The Lambda Model Of The Hybrid Superstring
• The Structure of Non-Abelian Kinks
• Giant Magnons of String Theory in the Lambda Background
• Boost generator in AdS_3 integrable superstrings for general braiding
• A study of integrable form factors in massless relativistic AdS_3
• Integrability of the $\lambda$-deformation of the PCM with spectators
• Quantum deformation of cubic string field theory
• Towards a quadratic Poisson algebra for the subtracted classical monodromy of Symmetric Space Sine-Gordon theories
• Multi-parametric R-matrix for the sl(2|1) Yangian