A New and Elementary CP^n Dyonic Magnon

We show that the dressing transformation method produces a new type of dyonic CP^n magnon in terms of which all the other known solutions are either composites or arise as special limits. In particular, this includes the embedding of Dorey's dyonic magnon via an RP^3 subspace of CP^n. We also show how to generate Dorey's dyonic magnon directly in the S^n sigma model via the dressing method without resorting to the isomorphism with the SU(2) principle chiral model when n=3. The new dyon is shown to be either a charged dyon or topological kink of the related symmetric-space sine-Gordon theories associated to CP^n and in this sense is a direct generalization of the soliton of the complex sine-Gordon theory.Comment: 21 pages, JHEP3, typos correcte

An integrable deformation of the AdS5×S5superstring

The S-matrix on the world-sheet theory of the string in AdS5 x S5 has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where q is real has been identified as a particular deformation of the Green-Schwarz sigma model. An interpretation of the case with q a root of unity has, until now, been lacking. We show that the Green-Schwarz sigma model admits a discrete deformation which can be viewed as a rather simple deformation of the F/F_V gauged WZW model, where F=PSU(2,2|4). The deformation parameter q is then a k-th root of unity where k is the level. The deformed theory has the same equations-of-motion as the Green-Schwarz sigma model but has a different symplectic structure. We show that the resulting theory is integrable and has just the right amount of kappa-symmetries that appear as a remnant of the fermionic part of the original gauge symmetry. This points to the existence of a fully consistent deformed string background.Comment: 23 pages, improved and expanded discussion of metric and B fiel

S-matrices and quantum group symmetry of k-deformed sigma models

Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with q=exp(i pi/k) a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum grou

On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models

This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/1-.1088/1751-8113/49/41/415402. © 2016 IOP Publishing Ltd.Yang–Baxter type models are integrable deformations of integrable field theories, such as the principal chiral model on a Lie group G or σ-models on (semi-)symmetric spaces G/F. The deformation has the effect of breaking the global G-symmetry of the original model, replacing the associated set of conserved charges by ones whose Poisson brackets are those of the q-deformed Poisson–Hopf algebra Uq ( ) g . Working at the Hamiltonian level, we show how this q-deformed Poisson algebra originates from a Poisson–Lie G-symmetry. The theory of Poisson–Lie groups and their actions on Poisson manifolds, in particular the formalism of the non-abelian moment map, is reviewed. For a coboundary Poisson–Lie group G, this non-abelian moment map must obey the Semenov-TianShansky bracket on the dual group G*, up to terms involving central quantities. When the latter vanish, we develop a general procedure linking this Poisson bracket to the defining relations of the Poisson–Hopf algebra Uq ( ) g , including the q-Poisson–Serre relations. We consider reality conditions leading to q being either real or a phase. We determine the nonabelian moment map for Yang–Baxter type models. This enables to compute the corresponding action of G on the fields parametrising the phase space of these models.Peer reviewe

The Curve of Compactified 6D Gauge Theories and Integrable Systems

We analyze the Seiberg-Witten curve of the six-dimensional N=(1,1) gauge theory compactified on a torus to four dimensions. The effective theory in four dimensions is a deformation of the N=2* theory. The curve is naturally holomorphically embedding in a slanted four-torus--actually an abelian surface--a set-up that is natural in Witten's M-theory construction of N=2 theories. We then show that the curve can be interpreted as the spectral curve of an integrable system which generalizes the N-body elliptic Calogero-Moser and Ruijsenaars-Schneider systems in that both the positions and momenta take values in compact spaces. It turns out that the resulting system is not simply doubly elliptic, rather the positions and momenta, as two-vectors, take values in the ambient abelian surface. We analyze the two-body system in some detail. The system we uncover provides a concrete realization of a Beauville-Mukai system based on an abelian surface rather than a K3 surface.Comment: 22 pages, JHEP3, 4 figures, improved readility of figures, added reference