The Analytic Structure of Trigonometric S Matrices

Abstract

$S$-matrices associated to the vector representations of the quantum groups for the classical Lie algebras are constructed. For the $a_{m-1}$ and $c_m$ algebras the complete $S$-matrix is found by an application of the bootstrap equations. It is shown that the simplest form for the $S$-matrix which generalizes that of the Gross-Neveu model is not consistent for the non-simply-laced algebras due to the existence of unexplained singularities on the physical strip. However, a form which generalizes the $S$-matrix of the principal chiral model is shown to be consistent via an argument which uses a novel application of the Coleman-Thun mechanism. The analysis also gives a correct description of the analytic structure of the $S$-matrix of the principle chiral model for $c_m$.

25 pages (macro included, 6 figures included as uuencoded compressed tar file), CERN-TH.6888/93, (An important argument is corrected leading to a novel application of the Coleman-Thun mechanism. Also decided to risk some figures.)

References in corpus (4)

• Quantum Solitons in Affine Toda Field Theories
• Exact S-Matrices for Nonsimply-Laced Affine Toda Theories
• Quantizing SL(N) Solitons and the Hecke Alegbra
• The full set of $c_n$-invariant factorized $S$-matrices

Cited by in corpus (17)

• On the Construction of Trigonometric Solutions of the Yang-Baxter Equation
• The Exact S-Matrix for an osp(2|2) Disordered System
• Integrable theories that are asymptotically CFT
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• A Relativistic Relative of the Magnon S-Matrix
• Critical RSOS Models in External Fields
• Exact S-Matrices with Affine Quantum Group Symmetry
• Exact S-matrices for d_{n+1}^{(2)} affine Toda solitons and their bound states
• Loop symmetry of integrable vertex models at roots of unity
• The Relativistic Avatars of Giant Magnons and their S-Matrix
• Quantum integrability of sigma models on AII and CII symmetric spaces
• Trigonometric S-Matrices, Affine Toda Solitons and Supersymmetry
• Exact Scattering in the SU(n) Supersymmetric Principal Chiral Model
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories
• From S-matrices to the Thermodynamic Bethe Ansatz
• Thermodynamic Bethe ansatz for the AII sigma-models