Yang-Baxter sigma models and Lax pairs arising from κ-Poincaré r-matrices

Abstract

Abstract: We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical r-matrices associated with κ-deformations of the Poincaré algebra. These classical κ-Poincaré r-matrices describe three kinds of deformations: 1) the standard deformation, 2) the tachyonic deformation, and 3) the light-cone deformation. For each deformation, the metric and two-form B-field are computed from the associated r-matrix. The first two deformations, related to the modified classical Yang-Baxter equation, lead to T-duals of dS4 and AdS4, respectively. The third deformation, associated with the homogeneous classical Yang-Baxter equation, leads to a time-dependent pp-wave background. Finally, we construct a Lax pair for the generalized κ-Poincaré r-matrix that unifies the three kinds of deformations mentioned above as special cases.