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

We study Yang-Baxter sigma models with deformed 4d Minkowski spacetimes arising from classical r-matrices associated with kappa-deformations of the Poincare algebra. These classical kappa-Poincare 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 dS(4) and AdS(4), 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 kappa-Poincare r-matrix that unifies the three kinds of deformations mentioned above as special cases.