An unexpected symmetry in the integrable structure of gauge and string theories and its root of unity limit

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K05059
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Osaka City University
• Principal Investigator: Oota Takeshi 大阪市立大学, 大学院理学研究科, 数学研究所専任研究所員 (70419688)
• Co-Investigator(Kenkyū-buntansha): 糸山 浩 大阪市立大学, 大学院理学研究科, 教授 (30243158) ; 吉岡 礼治 大阪市立大学, 大学院理学研究科, 博士研究員 (90514555)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 自由場表示 / 変形された量子対称性 / ベキ根極限

Outline of Final Research Achievements

The 2d/5d connection is a correspondence between certain two-dimensional field theories and five-dimensional gauge theories with supersymmetry. It implies that the correlation function of the two-dimensional theory and the partition function of the five-dimensional theory are the same. We have determined operators which give a free-field representation of the correlation function and showed that 2d/5d connection holds if the positions of the operators are slightly shifted.
The ``elliptic algebra’’ is a quantum symmetry whose structure constants are expressed in terms of the elliptic functions. We argued that this elliptic algebra plays important roles in the 2d/5d connection.

Free Research Field

数理物理