Probing local gravitational physics with Lorentzian singularities in field

2021 Fiscal Year Final Research Report

• Project/Area Number: 20K14465
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
• Research Institution: The University of Tokyo
• Principal Investigator: DODELSON MATTHEW 東京大学, カブリ数物連携宇宙研究機構, 特任研究員 (40835617)
• Project Period (FY): 2020-04-01 – 2022-03-31
• Keywords: String theory / black holes / conformal field theory / AdS/CFT / 二点関数

Outline of Final Research Achievements

The goal of this research project was to understand the possible singularities of the thermal two-point function in conformal field theories. A conformal field theory is a special kind of quantum field theory with no scale. The two-point function measures the correlation between two points in spacetime, and is singular when the two points can be connected by a light ray. Using the idea of holography, the thermal two-point function can be computed by considering fluctuations in a black hole background. Together with Hirosi Ooguri, we showed that there are naively new singularities in the two-point function due to light rays in the black hole background. These light rays can wrap around the black hole many times. However, one needs to take string theory into account to analyze this problem in full detail. By analysing the so-called Penrose limit of the spacetime, we were able to compute the full string-theoretic answer, and showed that the singularities are resolved in string theory.

Free Research Field

String theory

Academic Significance and Societal Importance of the Research Achievements

共形場理論は理論物理に普遍的に現れる重要な構造であり，実験的にはイジング模型の相転移点など二次相転移付近の物理に現れることが知られている．共形場理論を特徴づける量は相関関数であり，この構造を理解することが重要である．一方，本研究まではどのような特異点が二点関数に起こりえるかという疑問に精密な回答がなかったが，我々はこれまで知られていた特異点以外の特異点が発生しないことを示した．この研究によって，共形場理論の構造への理解が深まった．また，実験による検証可能性による新たな展開も存在する．共形場理論は理論物理以外の分野にも応用があるため，我々の結果はより広い文脈でも重要な可能性がある．