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Jae Hyung Yee - One of the best experts on this subject based on the ideXlab platform.

Hyeong-chan Kim - One of the best experts on this subject based on the ideXlab platform.

Chaiho Rim - One of the best experts on this subject based on the ideXlab platform.

Kentaroh Yoshida - One of the best experts on this subject based on the ideXlab platform.

  • yang baxter deformations of Minkowski Spacetime
    Journal of High Energy Physics, 2015
    Co-Authors: Takuya Matsumoto, Domenico Orlando, Susanne Reffert, Junichi Sakamoto, Kentaroh Yoshida
    Abstract:

    We study Yang-Baxter deformations of 4D Minkowski Spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincare group/Lorentz group. Instead we consider a slice of AdS5 by embedding the 4D Poincare group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.

Hideki Ishihara - One of the best experts on this subject based on the ideXlab platform.

  • Exactly solvable strings in Minkowski Spacetime
    Classical and Quantum Gravity, 2010
    Co-Authors: Hiroshi Kozaki, Tatsuhiko Koike, Hideki Ishihara
    Abstract:

    We study the integrability of the equations of motion for the Nambu–Goto strings with a cohomogeneity-one symmetry in Minkowski Spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion reduce to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For types I to VI, the integrability comes from the existence of Killing vectors on the orbit space which are the projections of Killing vectors on Minkowski Spacetime. For type VII, the integrability is related to a projected Killing vector and a nontrivial Killing tensor on the orbit space. We also find that the geodesic equations of all types are exactly solvable, and show the solutions.

  • exactly solvable strings in Minkowski Spacetime
    arXiv: General Relativity and Quantum Cosmology, 2009
    Co-Authors: Hiroshi Kozaki, Tatsuhiko Koike, Hideki Ishihara
    Abstract:

    We study the integrability of the equations of motion for the Nambu-Goto strings with a cohomogeneity-one symmetry in Minkowski Spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion can be reduced to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (Types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For Types I to VI, the integrability comes from the existence of Killing vectors on the orbit space which are the projections of Killing vectors on Minkowski Spacetime. For Type VII, the integrability is related to a projected Killing vector and a nontrivial Killing tensor on the orbit space. We also find that the geodesic equations of all types are exactly solvable, and show the solutions.