松本 高興

A bstract It is well-known that the partition function of the Jackiw-Teitelboim (JT) gravity is obtained by an integral transformation of volumes of moduli spaces for Riemann surfaces, also known as the Weil-Petersson volumes. This fact enables us to compute the perturbative genus expansion of the partition function by solving a KdV-type non-linear partial differential equation. In this work, we find that this KdV equation also admits transseries solutions. We give a systematic algorithm to explicitly construct a one-parameter transseries solution to the KdV equation. Our approach is based on general two-dimensional topological gravity, and the results for the JT gravity are easily obtained as a special case. The results in the leading non-perturbative sector perfectly agree with another independent calculation from topological recursions in random matrices.

A bstract We consider the Courant-Hilbert (CH) construction of integrable deformations of a two-dimensional principal chiral model (2D PCM) in the context of the four-dimensional Chern-Simons (4D CS) theory. According to this construction, an integrable deformation of 2D PCM is characterized by a boundary function. As a result, the master formula obtained from the 4D CS theory should be corrected by the trace of the energy-momentum tensor so as to support the CH construction. We present some examples of deformation including the $$T\overline{T }$$ -deformation, the root $$T\overline{T }$$ -deformation, the two-parameter mixed deformation, and a logarithmic deformation. Finally, we discuss some generalizations and potential applications of this CH construction.

Abstract 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.