Construction of higher dimensional spacetime from field theories with the gradient flow

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03620
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
• Research Institution: Osaka University
• Principal Investigator: Onogi Tetsuya 大阪大学, 大学院理学研究科, 教授 (70211802)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 高次元 / フロー方程式 / 一般相対論 / 保存量

Outline of Final Research Achievements

The purpose of this research is to construct higher-dimensional spacetime from field theory using flow equation.we also obtained research results.
1) In the d-dimensional massless scalar field theory, we obtain a spacetime with no event horizon and exotic matter field energy-momentum tensor for finite temperature. In addition,we proposed "Special Flow", which is an extension of the Flow equation. The space-time constructed using this clearly has the isometry of the AdS space as symmetry.
2)We studied energy conservation in general relativity. We show that the energy-momentum tensor multiplied by a new class of vector fields gives conserved quantities without global symmetry, and that such vector fields can always be constructed. We showed that the homogeneous isotropic universe satisfies the first law of thermodynamics, which can be interpreted as entropy. Furthermore, as an extension of this research, a comparison with conventional quasi-local energies was made.

Free Research Field

素粒子論

Academic Significance and Societal Importance of the Research Achievements

AdS/CFT対応の場の理論からの理解につながると期待されるフロー方程式とその拡張によって様々な結果が得られた。特にGKP-Witten関係式を場の理論から導出したことは今後の発展につながると期待される。また副産物として得られた一般相対性理論における新しいエネルギー保存量を発見した。従来に知られていた保存量とは独立な保存量で重力系に対して新しい知見を与えると期待される。