Selection of quantum field theories by chaos and superstring theory

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13483
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Osaka University
• Principal Investigator: Hashimoto Koji 大阪大学, 理学研究科, 教授 (80345074)
• Co-Investigator(Renkei-kenkyūsha): Yoshida Kentaroh 京都大学, 大学院理学系研究科, 助教 (30544928) ; SASA Shin-ichi 京都大学, 大学院理学系研究科, 教授 (30235238)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: カオス / 超弦理論 / 場の量子論

Outline of Final Research Achievements

We have performed a classical chaos analysis in the linear sigma model which is a low energy effective theory of QCD. We have found that the chaos appears when the spatially homogeneous configuration of the linear sigma model field has an energy density which is roughly equal to the energy scale of QCD phase transition at finite temperature. This result shows, first that, the chaos analysis is in general possible for strong coupling quantum theories, and second, that the chaos analysis of gauge invariant operator is possible. Furthermore, we have used the AdS/CFT correspondence to analyze the chaos for strongly coupled supersymmetric Yang-Mills and QCD. The Lyapunov exponent, which shows the strength of the chaos, is explicitly calculated, and is found to show a scaling law according to the rank of the gauge group and the coupling constant of the theory. In fact, the Lyapunov exponent decreases for larger N.

Free Research Field

超弦理論