Probing quantum spacetime structure via exact results of gauge theories

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K03845
• 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: Shinshu University
• Principal Investigator: Okuyama Kazumi 信州大学, 学術研究院理学系, 教授 (70447720)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: JT重力 / 行列模型 / 量子重力

Outline of Final Research Achievements

In collaboration with Kazuhiro Sakai, we have studied the matrix model of JT gravity, which is very useful as a toy model of quantum gravity because its description by the matrix model gives a non-perturbative definition of quantum gravity. We show that JT gravity is a special case of two-dimensional topological gravity, corresponding to a background with an infinite number of coupling constants chosen to some special value, and we develop a method for computing the genus expansion of the partition function recursively.

Free Research Field

素粒子理論、超弦理論

Academic Significance and Societal Importance of the Research Achievements

自然界の４つの力（電磁気力、弱い力、強い力、重力）のうち、重力だけが未だに量子論的な記述がわかっていない。超弦理論が量子重力の有力な候補であるが、弦理論では量子重力の非摂動的な効果を見ることが困難であるため、具体的に計算可能なトイモデルを調べることが重要である。JT重力の行列模型はそのようなトイモデルの中でもホログラフィー原理との相性が良く、本研究は量子重力の理解へ向けた重要な一歩である。