Fundamentals of 3-Dimensional Conformal Field Theory and Their Applications to Statistical Physics

2016 Fiscal Year Final Research Report

• Project/Area Number: 15K13540
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Okinawa Institute of Science and Technology Graduate University
• Principal Investigator: Shimada Hirohiko 沖縄科学技術大学院大学, 数理理論物理学ユニット, 研究員 (20751192)
• Co-Investigator(Renkei-kenkyūsha): HIKAMI Shinobu 沖縄科学技術大学院大学, 数理理論物理学ユニット, 教授 (30093298)
• Project Period (FY): 2015-04-01 – 2017-03-31
• Keywords: 3次元共形場理論 / くりこみ群のフロー / 普遍性クラス / 高分子のフラクタル次元 / 共形ブートストラップ / 自己回避ランダムウォーク (高分子) / 非ユニタリCFT / 無限振幅階層性

Outline of Final Research Achievements

Molecules tend to form a gas or a liquid when many of them gather together. Statistical physics aims to explain how such a system behaves non-trivially when many degrees of freedom interact with each other. Conformal field theory describes such systems well when the fluctuation becomes universal, for which, however, sensible understanding has remained elusive in three dimensions until recently. We reexamine the key assumption called unitarity and find that the 3d conformal field theory is much more versatile than it was thought to be. As an application, we have estimated that the universal fractal dimension of a polymer chain in a good solvent is about 1.7016.

Free Research Field

統計場の理論