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The Relativistic Avatars of Giant Magnons and their S-Matrix
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.Comment: 33 pages, important correction to S-matrix to ensure crossing
symmetr