量子不変量と場の理論の相互連関に関する研究

量子不变量与场论相互关系的研究

• 批准号: 21J10271
• 负责人: 森 祥仁
• 金额: $ 0.96万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2021
• 资助国家: 日本
• 起止时间: 2021-04-28 至 2023-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-21J10271/
• 关键词: 量子不変量; 色付きJones多項式; ADO不変量; WRT不変量; CGP不変量; Homological block; 量子モジュラー形式

本年度はWRT不変量とCGP不変量の間に関係式を証明するために, 2種類の絡み目不変量を研究した. small quantum group の表現を用いて構成される不変量を Reshetikhin--Turaev 不変量と呼び, unrolled quantum group の表現から構成される不変量をre-normalised Reshetikhin--Turaev 不変量と呼ぶ. WRT 不変量と CGP 不変量はそれぞれ Reshetikhin--Turaev 不変量と re-normalised Reshetikhin--Turaev 不変量から構成される. したがって, WRT 不変量と CGP 不変量の関係式を与えるためにはこれらの絡み目不変量に関係式を与える必要がある.Costantino--Geer--Patureau-Mirand は結び目に対する re-normalised Reshetikhin--Turaev 不変量の留数が Reshetikhin--Turaev 不変量で与えられることを証明し, この関係式から WRT 不変量と CGP 不変量の関係式を導いた. このように結び目に対する研究はいくつか行われているが, 絡み目を扱った先行研究はほとんどない. その理由の一つは, re-normalised Reshetikhin--Turaev 不変量の振る舞いが結び目と絡み目とで大きく異なることである. 例えば絡み目に対する re-normalised Reshetikhin--Turaev 不変量は正則関数なので留数から関係式を導けない. 本年度の研究で re-normalised Reshetikhin--Turaev 不変量 と Reshetikhin--Turaev 不変量の関係式を plumbed 絡み目の場合へ拡張できた.

This year, the relationship between WRT and CGP is proved, and 2 kinds of network are studied. Small quantum group performance is composed of three different components: Reshetikhin--Turaev, unrolled quantum group performance is composed of three different components: Reshetikhin--Turaev, unrolled quantum group performance is composed of three different components: reshetikhin-Turaev, unrolled quantum group performance is composed of three different components: reshetikhin--Turaev, unrolled quantum group performance is composed of three different components: reshetikhin--Turaev, unrolled quantum group performance is composed of three components: Reshetikhin--Turaev, unrolled quantum group performance is composed of three components: Reshetikhin--Turaev, unrolled quantum group performance is composed of three components: reshetikhin- WRT constant and CGP constant are both composed of Reshetikhin--Turaev constant and re-normalised Reshetikhin--Turaev constant. Costantino--Geer--Patureau-Mirand is the relation between WRT and CGP.Costantino--Geer--Patureau-Mirand is the relation between WRT and CGP.Costantino--Geer-Patureau-Mirand is the relation between WRT and CGP. This is the first time that we've had a study on this topic. The reason for this is a reverse, re-normalised Reshetikhin--Turaev does not change the amount of vibration in the dance. For example, the re-normalised Reshetikhin--Turaev relation is derived from the re-normalised Reshetikhin--Turaev relation. This year's research is re-normalised Reshetikhin--Turaev invariance, Reshetikhin--Turaev invariance, and the relationship between Reshetikhin--Turaev invariance and Reshetikhin--Turaev invariance.

项目成果

Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs

单模管道 H 图的 Witten-Reshetikhin-Turaev 不变量、同调块和量子模形式

• DOI: 10.3842/sigma.2022.034
• 发表时间: 2022
• 期刊: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
• 作者: Yoneda Saki;Maruno Takahiro;Mori Asuka;Hioki Ayana;Nishiumi Haruka;Okada Rio;Murakami Makoto;Zekun Wang;Fukuhara Ayano;Itagaki Nozomi;Harauchi Yosuke;Adachi Satoru;Okuyama Kumi;Sawaguchi Taichi;Torisu Tetsuo;Uchiyama Susumu;村山雄紀;Mazaya Najmina;伊藤聡・斎藤英喜編;Saki Yoneda;村山雄紀;Akihito Mori and Yuya Murakami
• 通讯作者: Akihito Mori and Yuya Murakami

非Seifert多様体に対する量子不変量の関係式と量子モジュラー性

非Seifert流形的量子不变关系和量子模性

• 发表时间: 2021
• 作者: Satoko Tokunaga;Ed Potten;Yuta Nishikawa;and Yuki Sugiyama;Mazaya Najmina;村山雄紀;森祥仁・村上友哉
• 通讯作者: 森祥仁・村上友哉

Relations between Reshetikhin--Turaev and re-normalized link invariants

Reshetikhin--Turaev 与重整化链接不变量之间的关系

• 发表时间: 2023
• 作者: Yoneda Saki;Maruno Takahiro;Mori Asuka;Hioki Ayana;Nishiumi Haruka;Okada Rio;Murakami Makoto;Zekun Wang;Fukuhara Ayano;Itagaki Nozomi;Harauchi Yosuke;Adachi Satoru;Okuyama Kumi;Sawaguchi Taichi;Torisu Tetsuo;Uchiyama Susumu;村山雄紀;Mazaya Najmina;伊藤聡・斎藤英喜編;Saki Yoneda;村山雄紀;Akihito Mori and Yuya Murakami;Mazaya Najmina;栗田英彦編;Mazaya Najmina;村山雄紀;米田早紀;Akihito Mori
• 通讯作者: Akihito Mori

Plumbed 多様体に対する Witten-Reshetikhin-Turaev 不変量

管道流形的 Witten-Reshetikhin-Turaev 不变量

• 发表时间: 2022
• 作者: Yoneda Saki;Maruno Takahiro;Mori Asuka;Hioki Ayana;Nishiumi Haruka;Okada Rio;Murakami Makoto;Zekun Wang;Fukuhara Ayano;Itagaki Nozomi;Harauchi Yosuke;Adachi Satoru;Okuyama Kumi;Sawaguchi Taichi;Torisu Tetsuo;Uchiyama Susumu;村山雄紀;Mazaya Najmina;伊藤聡・斎藤英喜編;Saki Yoneda;村山雄紀;Akihito Mori and Yuya Murakami;Mazaya Najmina;栗田英彦編;Mazaya Najmina;村山雄紀;米田早紀;Akihito Mori;村山雄紀;森 祥仁;Mazaya Najmina;森祥仁;Mazaya Najmina;村山雄紀;森祥仁
• 通讯作者: 森祥仁

色付きJones多項式とADO不変量

有色琼斯多项式和 ADO 不变量

• 发表时间: 2022
• 作者: Yoneda Saki;Maruno Takahiro;Mori Asuka;Hioki Ayana;Nishiumi Haruka;Okada Rio;Murakami Makoto;Zekun Wang;Fukuhara Ayano;Itagaki Nozomi;Harauchi Yosuke;Adachi Satoru;Okuyama Kumi;Sawaguchi Taichi;Torisu Tetsuo;Uchiyama Susumu;村山雄紀;Mazaya Najmina;伊藤聡・斎藤英喜編;Saki Yoneda;村山雄紀;Akihito Mori and Yuya Murakami;Mazaya Najmina;栗田英彦編;Mazaya Najmina;村山雄紀;米田早紀;Akihito Mori;村山雄紀;森 祥仁
• 通讯作者: 森 祥仁