Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories

Abstract

We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal moduli space that can be identified with a particular co-adjoint orbit of the unbroken subgroup H of G. Classically the solitons come in a continuous spectrum which encompasses the perturbative fluctuations of the theory as the kink charge becomes small. We show that the solitons can be quantized by allowing the collective coordinates to be time-dependent to yield a form of quantum mechanics on the co-adjoint orbit. The quantum states correspond to symmetric tensor representations of the symmetry group H and have the interpretation of a fuzzy geometric version of the co-adjoint orbit. The quantized finite tower of soliton states includes the perturbative modes at the base.

53 pages, additional comments and small errors corrected, final journal version

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• Two-dimensional S-matrices from unitarity cuts
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• A Relativistic Relative of the Magnon S-Matrix
• Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• The Semi-Classical Spectrum of Solitons and Giant Magnons
• The Structure of Non-Abelian Kinks
• Symplectic Deformations of Integrable Field Theories and AdS/CFT
• Giant Magnons of String Theory in the Lambda Background
• Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction
• Two-loop corrections to partition function of Pohlmeyer-reduced theory for AdS_5 x S^5 superstring
• Integrability of the $\lambda$-deformation of the PCM with spectators
• Towards a quadratic Poisson algebra for the subtracted classical monodromy of Symmetric Space Sine-Gordon theories