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

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.