Bound State Scattering Simplified

Abstract

In the description of the AdS5/CFT4 duality by an integrable system the scattering matrix for bound states plays a crucial role: it was initially constructed for the evaluation of finite size corrections to the planar spectrum of energy levels/anomalous dimensions by the thermodynamic Bethe ansatz, and more recently it re-appeared in the context of the glueing prescription of the hexagon approach to higher-point functions. In this work we present a simplified form of this scattering matrix and we make its pole structure manifest. We find some new relations between its matrix elements and also present an explicit form for its inverse. We finally discuss some of its properties including crossing symmetry. Our results will hopefully be useful for computing finite-size effects such as the ones given by the complicated sum-integrals arising from the glueing of hexagons, as well as help towards understanding universal features of the AdS5/CFT4 scattering matrix.

arXiv comment17 pages; Mathematica notebook attached to the submission; v2: misprints and references corrected

References in corpus (26)

• Gauge Theory Correlators from Non-Critical String Theory
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Transcendentality and Crossing
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• The su(2|2) Dynamic S-Matrix
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• Foundations of the AdS_5 x S^5 Superstring. Part I
• Integrability for the Full Spectrum of Planar AdS/CFT
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Hexagonalization of Correlation Functions
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Tessellating cushions: four-point functions in N=4 SYM
• The S-matrix of String Bound States
• The Dressing Factor and Crossing Equations
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Bound States, Yangian Symmetry and Classical r-matrix for the AdS5 x S5 Superstring
• The S-Matrix of AdS/CFT and Yangian Symmetry
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Positivity of hexagon perturbation theory
• Universal blocks of the AdS/CFT Scattering Matrix
• Polylogarithms from the bound state S-matrix