S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models

Abstract

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 group symmetry.

32 pages, added reference, changed nomenclature from q deformed to k deformed to distinguish from eta deformation

References in corpus (13)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• On deformations of AdS_n x S^n supercosets
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• The all-loop non-Abelian Thirring model and its RG flow
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix

Cited by in corpus (25)

• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• Integrable Deformations of Sigma Models
• General phase spaces: from discrete variables to rotor and continuum limits
• Superintegrability of Geodesic Motion on the Sausage Model
• RG flows of integrable $\sigma$-models and the twist function
• Integrable Lambda Models And Chern-Simons Theories
• Integrable strings for AdS/CFT
• On the quantization of continuous non-ultralocal integrable systems
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Strong integrability of $\lambda$-deformed models
• Lambda Models From Chern-Simons Theories
• Exploring The Lambda Model Of The Hybrid Superstring
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• On strong integrability of the dressing cosets
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Novel integrable interpolations
• Asymptotics in an Asymptotic CFT
• Lax pairs on Yang-Baxter deformed backgrounds
• Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production
• A generalized 4d Chern-Simons theory
• Scale without conformal invariance from integrable deformations of coset CFTs
• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model