{"title":"Novel integrability in string theory from automorphic symmetries","authors":"A. V. Pribytok","doi":"10.1134/s0040577923120103","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We develop a technique based on the boost automorphism for finding new lattice integrable models with various dimensions of local Hilbert spaces. We initiate the method by implementing it in two-dimensional models and resolve a classification problem, which not only confirms the known vertex model solution space but also extends to the new <span>\\(\\mathfrak{sl}_2\\)</span> deformed sector. A generalization of the approach to integrable string backgrounds is provided and allows finding new integrable deformations and associated <span>\\(R\\)</span>-matrices. The new integrable solutions appear to be of a nondifference or pseudo-difference form admitting <span>\\(AdS_2\\)</span> and <span>\\(AdS_3\\)</span> <span>\\(S\\)</span>-matrices as special cases (embeddings), which also includes a map of the double-deformed sigma model <span>\\(R\\)</span>-matrix. The corresponding braiding and conjugation operators of the novel models are derived. We also demonstrate implications of the obtained free-fermion analogue for <span>\\(AdS\\)</span> deformations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577923120103","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We develop a technique based on the boost automorphism for finding new lattice integrable models with various dimensions of local Hilbert spaces. We initiate the method by implementing it in two-dimensional models and resolve a classification problem, which not only confirms the known vertex model solution space but also extends to the new \(\mathfrak{sl}_2\) deformed sector. A generalization of the approach to integrable string backgrounds is provided and allows finding new integrable deformations and associated \(R\)-matrices. The new integrable solutions appear to be of a nondifference or pseudo-difference form admitting \(AdS_2\) and \(AdS_3\)\(S\)-matrices as special cases (embeddings), which also includes a map of the double-deformed sigma model \(R\)-matrix. The corresponding braiding and conjugation operators of the novel models are derived. We also demonstrate implications of the obtained free-fermion analogue for \(AdS\) deformations.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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