{"title":"具有广义 F 结构的可积分西格玛模型、具有广义复合结构的杨-巴克斯特西格玛模型和多杨-巴克斯特西格玛模型","authors":"","doi":"10.1016/j.nuclphysb.2024.116671","DOIUrl":null,"url":null,"abstract":"<div><p>We construct an integrable sigma model with a generalized <span><math><mi>F</mi></math></span> structure, which involves a generalized Nijenhuis structure <span><math><mi>J</mi></math></span> satisfying <span><math><msup><mrow><mi>J</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mo>−</mo><mi>J</mi></math></span>. Utilizing the expression of the generalized complex structure on the metric Lie group manifold <em>G</em> in terms of operator relations on its Lie algebra <span><math><mi>g</mi></math></span>, we formulate a Yang-Baxter sigma model with a generalized complex structure. Additionally, we present multi-Yang-Baxter sigma models featuring two and three compatible Nijenhuis structures. Examples for each of these models are provided.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324002372/pdfft?md5=b11fed62dad4d217596d7079c9914fc1&pid=1-s2.0-S0550321324002372-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Integrable sigma model with generalized F structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model\",\"authors\":\"\",\"doi\":\"10.1016/j.nuclphysb.2024.116671\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We construct an integrable sigma model with a generalized <span><math><mi>F</mi></math></span> structure, which involves a generalized Nijenhuis structure <span><math><mi>J</mi></math></span> satisfying <span><math><msup><mrow><mi>J</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mo>−</mo><mi>J</mi></math></span>. Utilizing the expression of the generalized complex structure on the metric Lie group manifold <em>G</em> in terms of operator relations on its Lie algebra <span><math><mi>g</mi></math></span>, we formulate a Yang-Baxter sigma model with a generalized complex structure. Additionally, we present multi-Yang-Baxter sigma models featuring two and three compatible Nijenhuis structures. Examples for each of these models are provided.</p></div>\",\"PeriodicalId\":54712,\"journal\":{\"name\":\"Nuclear Physics B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0550321324002372/pdfft?md5=b11fed62dad4d217596d7079c9914fc1&pid=1-s2.0-S0550321324002372-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nuclear Physics B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0550321324002372\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, PARTICLES & FIELDS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0550321324002372","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
摘要
我们构建了一个具有广义 F 结构的可积分西格玛模型，它涉及满足 J3=-J 的广义尼延胡斯结构 J。利用广义复结构在度量烈群流形 G 上的表达式，即其烈代数 g 上的算子关系，我们提出了一个具有广义复结构的杨-巴克斯特西格玛模型。此外，我们还提出了多杨-巴克斯特西格玛模型，它具有两个和三个兼容的尼延胡斯结构。我们还提供了每个模型的示例。
Integrable sigma model with generalized F structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model
We construct an integrable sigma model with a generalized structure, which involves a generalized Nijenhuis structure satisfying . Utilizing the expression of the generalized complex structure on the metric Lie group manifold G in terms of operator relations on its Lie algebra , we formulate a Yang-Baxter sigma model with a generalized complex structure. Additionally, we present multi-Yang-Baxter sigma models featuring two and three compatible Nijenhuis structures. Examples for each of these models are provided.
期刊介绍：
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.
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