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Nonexplicit versions of integrable equations 积分方程的非显式版本
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-22 DOI: 10.1134/s0040577923120097
A. K. Pogrebkov
{"title":"Nonexplicit versions of integrable equations","authors":"A. K. Pogrebkov","doi":"10.1134/s0040577923120097","DOIUrl":"https://doi.org/10.1134/s0040577923120097","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider some generalizations of a <span>((2+1))</span>-dimensional Davey–Stewartson-type equation. In particular, we propose a dynamical system that does not admit an explicit formulation in terms of differential equations, but needs an additional independent variable. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139024098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new solvable two-matrix model and the BKP tau function 新的可解双矩阵模型和 BKP tau 函数
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-22 DOI: 10.1134/s0040577923120012
E. N. Antonov, A. Yu. Orlov
{"title":"A new solvable two-matrix model and the BKP tau function","authors":"E. N. Antonov, A. Yu. Orlov","doi":"10.1134/s0040577923120012","DOIUrl":"https://doi.org/10.1134/s0040577923120012","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We present exactly solvable modifications of the two-matrix Zinn-Justin–Zuber model and write it as a tau function. The grand partition function of these matrix integrals is written as the fermion expectation value. The perturbation theory series is written explicitly in terms of a series in strict partitions. The related string equations are presented. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139025414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sigma models as Gross–Neveu models. II 作为格罗斯-涅乌模型的西格玛模型。二
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-22 DOI: 10.1134/s0040577923120048
D. V. Bykov
{"title":"Sigma models as Gross–Neveu models. II","authors":"D. V. Bykov","doi":"10.1134/s0040577923120048","DOIUrl":"https://doi.org/10.1134/s0040577923120048","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We summarize some (mostly geometric) facts underlying the relation between <span>(2)</span>D integrable sigma models and generalized Gross–Neveu models, emphasizing connections to the theory of nilpotent orbits, Springer resolutions, and quiver varieties. This is meant to shed light on the general setup when this correspondence holds. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Novel integrability in string theory from automorphic symmetries 从自动对称性看弦理论中的新可整性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-22 DOI: 10.1134/s0040577923120103
A. V. Pribytok
{"title":"Novel integrability in string theory from automorphic symmetries","authors":"A. V. Pribytok","doi":"10.1134/s0040577923120103","DOIUrl":"https://doi.org/10.1134/s0040577923120103","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":1.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The structure of quantum corrections and exact results in supersymmetric theories from the higher covariant derivative regularization 从高协变导数正则化看超对称理论的量子修正结构和精确结果
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-22 DOI: 10.1134/s0040577923120127
K. V. Stepanyantz
{"title":"The structure of quantum corrections and exact results in supersymmetric theories from the higher covariant derivative regularization","authors":"K. V. Stepanyantz","doi":"10.1134/s0040577923120127","DOIUrl":"https://doi.org/10.1134/s0040577923120127","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We review some recent results of the studies of quantum corrections in supersymmetric theories derived using Slavnov’s higher covariant derivative regularization. In particular, we demonstrate that the <span>(beta)</span>-function of <span>(mathcal{N}=1)</span> supersymmetric theories is related to the anomalous dimensions of matter superfields by the NSVZ relation if the theory is regularized by higher covariant derivatives and the renormalization group functions are defined in terms of the bare couplings, because the corresponding loop corrections are given by integrals of double total derivatives in the momentum space. For the standard renormalization-group functions, we show that an all-loop NSVZ renormalization scheme is given by the HD<span>(,+,)</span>MSL renormalization prescription when the higher covariant derivative regularization is supplemented by minimal subtractions of logarithms. Applications of these results to the precise calculations in various supersymmetric theories are briefly described. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139023902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Poincaré–Birkhoff–Witt basis of the quantum general linear superalgebra 论量子通用线性上代数的波恩卡莱-伯克霍夫-维特基础
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1134/s0040577923120115
A. V. Razumov
{"title":"On Poincaré–Birkhoff–Witt basis of the quantum general linear superalgebra","authors":"A. V. Razumov","doi":"10.1134/s0040577923120115","DOIUrl":"https://doi.org/10.1134/s0040577923120115","url":null,"abstract":"","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139019841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonexplicit versions of integrable equations 积分方程的非显式版本
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1134/s0040577923120097
A. Pogrebkov
{"title":"Nonexplicit versions of integrable equations","authors":"A. Pogrebkov","doi":"10.1134/s0040577923120097","DOIUrl":"https://doi.org/10.1134/s0040577923120097","url":null,"abstract":"","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139024856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cluster variables for affine Lie–Poisson systems 仿射李-泊松系统的簇变量
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1134/s0040577923120140
L. O. Chekhov
{"title":"Cluster variables for affine Lie–Poisson systems","authors":"L. O. Chekhov","doi":"10.1134/s0040577923120140","DOIUrl":"https://doi.org/10.1134/s0040577923120140","url":null,"abstract":"","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139020598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher spins in harmonic superspace 谐波超空间中的高级自旋
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1134/s004057792312005x
{"title":"Higher spins in harmonic superspace","authors":"","doi":"10.1134/s004057792312005x","DOIUrl":"https://doi.org/10.1134/s004057792312005x","url":null,"abstract":"<span> <h3>Abstract</h3> <p> We report on a recent progress in constructing off-shell <span> <span>(4)</span> </span>D, <span> <span>(mathcal{N}=2)</span> </span> supersymmetric integer higher-superspin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with matter hypermultiplets. For even superspins, a new equivalent representation of the hypermultiplet couplings in terms of an analytic <span> <span>(omega)</span> </span> superfield is presented. It involves both cubic and quartic vertices. </p> </span>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139023903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Action of the monodromy matrix elements in the generalized algebraic Bethe ansatz 广义代数贝特方差中单色矩阵元素的作用
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1134/s0040577923120085
G. Kulkarni, N. Slavnov
{"title":"Action of the monodromy matrix elements in the generalized algebraic Bethe ansatz","authors":"G. Kulkarni, N. Slavnov","doi":"10.1134/s0040577923120085","DOIUrl":"https://doi.org/10.1134/s0040577923120085","url":null,"abstract":"","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139019346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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