Yang-Baxter deformations of the flat space string

Abstract

We define integrability preserving Yang-Baxter deformations of symmetric space sigma models with non-semi-simple symmetry group, in particular the flat space string, using only the essential structures of a symmetric space sigma model. For homogeneous deformations, the Lax connection is of the same form as the semi-simple case, although the R operator no longer satisfies a freestanding operator equation. For inhomogeneous deformations, the form of the Lax connection needs to be relaxed, by modifying the underlying algebra. We illustrate the construction by discussing nonabelian deformations of three dimensional Minkowski space.

8 pages

References in corpus (9)

• Quantum Deformations of the One-Dimensional Hubbard Model
• Abelian Yang-Baxter Deformations and TsT transformations
• Yang-Baxter sigma models based on the CYBE
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Anyons from Strings
• Unimodular jordanian deformations of integrable superstrings