2015/10/31 by Andrzej Borowiec, Hideki Kyono, Jerzy Lukierski +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homogeneous #Lax pair #Metric (unit) #Minkowski space #Noncommutative and Quantum Gravity Theories #Sigma #Sigma model #gr-qc #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/jhep04(2016)079
31 pages, v2: some clarifications and references added, published version
openalex publication_date 2016/04/01 · arxiv created 2016/04/20 · arxiv updated 2016/05/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.