The Relativistic Avatars of Giant Magnons and their S-Matrix

Abstract

The motion of strings on symmetric space target spaces underlies the integrability of the AdS/CFT correspondence. Although these theories, whose excitations are giant magnons, are non-relativistic they are classically equivalent, via the Polhmeyer reduction, to a relativistic integrable field theory known as a symmetric space sine-Gordon theory. These theories can be formulated as integrable deformations of gauged WZW models. In this work we consider the class of symmetric spaces CP^{n+1} and solve the corresponding generalized sine-Gordon theories at the quantum level by finding the exact spectrum of topological solitons, or kinks, and their S-matrix. The latter involves a trignometric solution of the Yang-Baxer equation which exhibits a quantum group symmetry with a tower of states that is bounded, unlike for magnons, as a result of the quantum group deformation parameter q being a root of unity. We test the S-matrix by taking the semi-classical limit and comparing with the time delays for the scattering of classical solitons. We argue that the internal CP^{n-1} moduli space of collective coordinates of the solitons in the classical theory can be interpreted as a q-deformed fuzzy space in the quantum theory. We analyse the n=1 case separately and provide a further test of the S-matrix conjecture in this case by calculating the central charge of the UV CFT using the thermodynamic Bethe Ansatz.

33 pages, important correction to S-matrix to ensure crossing symmetry

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Cited by in corpus (13)

• An Integrable Deformation of the AdS5 x S5 Superstring
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• 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
• On the perturbative S-matrix of generalized sine-Gordon models
• Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories
• The Semi-Classical Spectrum of Solitons and Giant Magnons
• The Structure of Non-Abelian Kinks
• 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
• Towards a quadratic Poisson algebra for the subtracted classical monodromy of Symmetric Space Sine-Gordon theories