Kentaroh Yoshida

A bstract: We present integrable deformations of Yang-Baxter (YB) sigma models based on the Courant-Hilbert (CH) construction. To this end, we employ the four-dimensional Chern-Simons theory, in which the CH construction is shown in arXiv:2509.22080. As a result, the CH construction works in an intricate way alongside the YB deformations. Remarkably, the resulting deformed action can also be expressed as the sum of the master formula Lagrangian and the trace of the energy-momentum tensor. This result indicates the universality of the correction term.

A bstract: We study oscillons in a real scalar field theory in a (3+1)-dimensional AdS space with global coordinates. The initial configuration is given by a Gaussian shape with an appropriate core size as in Minkowski spacetime. The solution exhibits a long lifetime. In particular, since the AdS space can be seen as a box, the recurrence phenomenon can be observed under suitable conditions. In particular, as the AdS radius decreases, one can see a transition from a metastable oscillon to a stable oscillatory solution. Finally, we discuss some potential applications of the oscillon in the context of AdS/CFT duality.

We study the origin of turbulence on the string worldsheet with boundaries laid in anti de Sitter (AdS) spacetime. While the classical motion of a single closed string in AdS is integrable, it has recently been recognized that weak turbulence arises in the case of an open string suspended from the AdS boundary. In the open string case, it is necessary to impose boundary conditions on the worldsheet boundaries. We classify which boundary conditions preserve integrability. Based on this classification, we anticipate that turbulence may occur on the string worldsheet if integrability is not guaranteed by the boundary conditions. Numerical investigations of the classical open-string dynamics support that turbulence occurs when the boundary conditions are not integrable.

We study the origin of turbulence on the string worldsheet with boundaries laid in anti de Sitter (AdS) spacetime. While the classical motion of a single closed string in AdS is integrable, it has recently been recognized that weak turbulence arises in the case of an open string suspended from the AdS boundary. In the open string case, it is necessary to impose boundary conditions on the worldsheet boundaries. We classify which boundary conditions preserve integrability. Based on this classification, we anticipate that turbulence may occur on the string worldsheet if integrability is not guaranteed by the boundary conditions. Numerical investigations of the classical open-string dynamics support that turbulence occurs when the boundary conditions are not integrable.

We revisit classical string motion in a near pp-wave limit of AdS₅ × S⁵. It is known that the Toda lattice models are integrable. But if the exponential potential is truncated at finite order, then the system may become non-integrable. In particular, when the exponential potential in a three-particle periodic Toda chain is truncated at the third order of the dynamical variables, the resulting system becomes a well-known non-integrable system, Henon-Heiles model. The same thing may happen in a near pp-wave limit of AdS₅ × S⁵, on which the classical string motion becomes chaotic.

Chaotic scattering is a manifestation of transient chaos realized by the scattering with non-integrable potential. When the initial position is taken in the potential, a particle initially exhibits chaotic motion, but escapes outside after a certain period of time. The time to stay inside the potential can be seen as lifetime and this escape process may be regarded as a kind of instability. The process of this type exists in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model in which the potential has flat directions. We discuss this chaotic instability by reducing the system with an ansatz to a simple dynamical system and present the associated fractal structure. We also show the singular behavior of the time delay function and compute the fractal dimension. This chaotic instability is the basic mechanism by which membranes are unstable, which is also common to supermembranes at quantum level.

Chaotic scattering is a manifestation of transient chaos realized by the scattering with non-integrable potential. When the initial position is taken in the potential, a particle initially exhibits chaotic motion, but escapes outside after a certain period of time. The time to stay inside the potential can be seen as lifetime and this escape process may be regarded as a kind of instability. The process of this type exists in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model in which the potential has flat directions. We discuss this chaotic instability by reducing the system with an ansatz to a simple dynamical system and present the associated fractal structure. We also show the singular behavior of the time delay function and compute the fractal dimension. This chaotic instability is the basic mechanism by which membranes are unstable, which is also common to supermembranes at quantum level.