Crossing and Antisolitons in Affine Toda Theories

Abstract

Affine Toda theory is a relativistic integrable theory in two dimensions possessing solutions describing a number of different species of solitons when the coupling is chosen to be imaginary. These nevertheless carry real energy and momentum. To each species of soliton there has to correspond an antisoliton species. There are two different ways of realising the antisoliton whose equivalence is shown to follow from a surprising identity satisfied within the underlying affine Kac-Moody group. This is the classical analogue of the crossing property of analytic S-matrix theory. Since a complex parameter related to the coordinate of the soliton is inverted, this identity implies a sort of modular transformation property of the soliton solution. The results simplify calculations of explicit soliton solutions.

20 pages, PLAIN TEX (changed macro!!), SWAT/92-93/6

References in corpus (2)

• Quantum Solitons in Affine Toda Field Theories
• Affine Toda Solitons and Automorphisms of Dynkin Diagrams

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• Multi--Soliton Solutions of Affine Toda Models
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• Toda Soliton Mass Corrections and the Particle--Soliton Duality Conjecture
• Minimal surfaces in AdS space and Integrable systems
• Solitons and Vertex Operators in Twisted Affine Toda Field Theories
• BPS Z(N) String Tensions, Sine Law and Casimir Scaling and Integrable Field Theories
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories
• Restricted Quantum Theory of Affine Toda Solitons
• $A_n^{(1)}$ Toda solitons and the dressing symmetry
• Reality of Complex Affine Toda Solitons
• Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in Affine Toda Field Theories
• N-Extended Lorentzian Kac-Moody algebras
• Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations