Emergence of Integrability in Gauge Theory and Random Geometry Probed by Matrix and Tensor Models

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03828
• 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 Metropolitan University (2022-2023); Osaka City University (2019-2021)
• Principal Investigator: Itoyama Hiroshi (糸山浩司) 大阪公立大学, 南部陽一郎物理学研究所, 特任教授 (30243158)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: unitary matrix model / discrete Painleve system / critical hypersurfaces / tensorial characters

Outline of Final Research Achievements

matrix model:with regard to the critical phenomena in the AD vicinity,on the basis of the fact that finite N matrix model is given by the discrete Painleve system,we showed that the unitary matrix model of this type provide theory space to thiscritical phenomena. In the space of mass parameters, We showed explicitly that AD singularities form hypersurfaces in general. We derived explicitly that AD singularities form hypersurfaces in the space of mass parameters.tensor model: we established operator VS Feynman diagram correspondence, introduced a tensorial character constructed a generalized cut operation associated with higher order variations.

Free Research Field

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Academic Significance and Societal Importance of the Research Achievements

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