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Two homomorphisms from the affine Yangian associated with (widehat{mathfrak {sl}}(n)) to the affine Yangian associated with (widehat{mathfrak {sl}}(n+1)) 从与(widehat{mathfrak {sl}}(n)) 相关的仿射杨格到与(widehat{mathfrak {sl}}(n+1)) 相关的仿射杨格的两个同态关系
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-14 DOI: 10.1007/s11005-024-01879-9
Mamoru Ueda
{"title":"Two homomorphisms from the affine Yangian associated with (widehat{mathfrak {sl}}(n)) to the affine Yangian associated with (widehat{mathfrak {sl}}(n+1))","authors":"Mamoru Ueda","doi":"10.1007/s11005-024-01879-9","DOIUrl":"10.1007/s11005-024-01879-9","url":null,"abstract":"<div><p>We construct a homomorphism from the affine Yangian <span>(Y_{hbar ,varepsilon +hbar }(widehat{mathfrak {sl}}(n)))</span> to the affine Yangian <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1)))</span> which is different from the one in Ueda (A homomorphism from the affine Yangian <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n)))</span> to the affine Yangian <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1)))</span>, 2023. arXiv:2312.09933). By using this homomorphism, we give a homomorphism from <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n))otimes Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m)))</span> to <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(m+n)))</span>. As an application, we construct a homomorphism from the affine Yangian <span>(Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m)))</span> to the centralizer algebra of the pair of affine Lie algebras <span>((widehat{mathfrak {gl}}(m+n),widehat{mathfrak {sl}}(n)))</span> and the coset vertex algebra of the pair of rectangular <i>W</i>-algebras <span>(mathcal {W}^k(mathfrak {gl}(2m+2n),(2^{m+n})))</span> and <span>(mathcal {W}^{k+m}(mathfrak {sl}(2n),(2^{n})))</span>.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the (L^2)-subcritical case 具有库仑势的费米子非线性薛定谔系统的基态 I：(L^2)-次临界情况
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-14 DOI: 10.1007/s11005-024-01877-x
Bin Chen, Yujin Guo
{"title":"Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the (L^2)-subcritical case","authors":"Bin Chen,&nbsp;Yujin Guo","doi":"10.1007/s11005-024-01877-x","DOIUrl":"10.1007/s11005-024-01877-x","url":null,"abstract":"<div><p>We consider ground states of the <i>N</i> coupled fermionic nonlinear Schrödinger systems with the Coulomb potential <i>V</i>(<i>x</i>) in the <span>(L^2)</span>-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter <span>(alpha &gt;0)</span>, which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as <span>(alpha rightarrow infty )</span>, where the mass concentrates at one of the singular points for the Coulomb potential <i>V</i>(<i>x</i>).\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Quantum intersection numbers and the Gromov–Witten invariants of ({{{mathbb {C}}}{{mathbb {P}}}}^1) 量子交集数和（{{mathbb {C}}}{{mathbb {P}}}}^1) ）的格罗莫夫-维滕不变式
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-13 DOI: 10.1007/s11005-024-01869-x
Xavier Blot, Alexandr Buryak
{"title":"Quantum intersection numbers and the Gromov–Witten invariants of ({{{mathbb {C}}}{{mathbb {P}}}}^1)","authors":"Xavier Blot,&nbsp;Alexandr Buryak","doi":"10.1007/s11005-024-01869-x","DOIUrl":"10.1007/s11005-024-01869-x","url":null,"abstract":"<div><p>The notion of a quantum tau-function for a natural quantization of the KdV hierarchy was introduced in a work of Dubrovin, Guéré, Rossi, and the second author. A certain natural choice of a quantum tau-function was then described by the first author, the coefficients of the logarithm of this series are called the quantum intersection numbers. Because of the Kontsevich–Witten theorem, a part of the quantum intersection numbers coincides with the classical intersection numbers of psi-classes on the moduli spaces of stable algebraic curves. In this paper, we relate the quantum intersection numbers to the stationary relative Gromov–Witten invariants of <span>(({{{mathbb {C}}}{{mathbb {P}}}}^1,0,infty ))</span> with an insertion of a Hodge class. Using the Okounkov–Pandharipande approach to such invariants (with the trivial Hodge class) through the infinite wedge formalism, we then give a short proof of an explicit formula for the “purely quantum” part of the quantum intersection numbers, found by the first author, which in particular relates these numbers to the one-part double Hurwitz numbers.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Framed cohomological Hall algebras and cohomological stable envelopes 框架上同调霍尔代数与上同调稳定包络。
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2023-09-11 DOI: 10.1007/s11005-023-01716-5
Tommaso Maria Botta
{"title":"Framed cohomological Hall algebras and cohomological stable envelopes","authors":"Tommaso Maria Botta","doi":"10.1007/s11005-023-01716-5","DOIUrl":"10.1007/s11005-023-01716-5","url":null,"abstract":"<div><p>There are multiple conjectures relating the cohomological Hall algebras (CoHAs) of certain substacks of the moduli stack of representations of a quiver <i>Q</i> to the Yangian <span>(Y^{Q}_textrm{MO})</span> by Maulik–Okounkov, whose construction is based on the notion of stable envelopes of Nakajima varieties. In this article, we introduce the cohomological Hall algebra of the moduli stack of framed representations of a quiver <i>Q</i> (framed CoHA), and we show that the equivariant cohomology of the disjoint union of the Nakajima varieties <span>({mathcal {M}}_Q(text {v},text {w}))</span> for all dimension vectors <span>(text {v})</span> and framing vectors <span>(text {w})</span> has a canonical structure of subalgebra of the framed CoHA. Restricted to this subalgebra, the algebra multiplication is identified with the stable envelope map. As a corollary, we deduce an explicit inductive formula to compute stable envelopes in terms of tautological classes.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"113 5","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10495305/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10235533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(C_2) generalization of the van Diejen model from the minimal ((D_5,D_5)) conformal matter 最小(D5,D5)共形物质对van Diejen模型的C2推广。
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1007/s11005-023-01714-7
Belal Nazzal, Anton Nedelin
{"title":"(C_2) generalization of the van Diejen model from the minimal ((D_5,D_5)) conformal matter","authors":"Belal Nazzal,&nbsp;Anton Nedelin","doi":"10.1007/s11005-023-01714-7","DOIUrl":"10.1007/s11005-023-01714-7","url":null,"abstract":"<div><p>We study superconformal indices of 4<i>d</i> compactifications of the 6<i>d</i> minimal <span>((D_{N+3},D_{N+3}))</span> conformal matter theories on a punctured Riemann surface. Introduction of supersymmetric surface defect in these theories is done at the level of the index by the action of the finite difference operators on the corresponding indices. There exist at least three different types of such operators according to three types of punctures with <span>(A_N, C_N)</span> and <span>(left( A_1right) ^N)</span> global symmetries. We mainly concentrate on <span>(C_2)</span> case and derive explicit expression for an infinite tower of difference operators generalizing the van Diejen model. We check various properties of these operators originating from the geometry of compactifications. We also provide an expression for the kernel function of both our <span>(C_2)</span> operator and previously derived <span>(A_2)</span> generalization of van Diejen model. Finally, we also consider compactifications with <span>(A_N)</span>-type punctures and derive the full tower of commuting difference operators corresponding to this root system generalizing the result of our previous paper.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"113 5","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10480275/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10191033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A local rigidity theorem for minimal two-spheres in charged time-symmetric initial data set 带电时间对称初始数据集最小两球的局部刚性定理
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2023-08-30 DOI: 10.1007/s11005-023-01713-8
H. Baltazar, A. Barros, R. Batista
{"title":"A local rigidity theorem for minimal two-spheres in charged time-symmetric initial data set","authors":"H. Baltazar,&nbsp;A. Barros,&nbsp;R. Batista","doi":"10.1007/s11005-023-01713-8","DOIUrl":"10.1007/s11005-023-01713-8","url":null,"abstract":"<div><p>The purpose of this article is to prove that, under suitable constraints on time-symmetric initial data set for the Einstein–Maxwell equation <i>M</i>, if <span>(Sigma subset M)</span> is an embedded strictly stable minimal two-sphere which locally maximizes the charged Hawking mass, then there exists a neighborhood of it in <i>M</i> isometric to the Reissner–Nordström–de Sitter space. At the same time, motivated (Bray et al. in Commun Anal Geom 18(4):821–830, 2010), we will deduce an estimate for the area of a two-sphere which is locally area minimizing on time-symmetric initial data set for the Einstein–Maxwell equation. Moreover, if the equality holds, then there exists a neighborhood of it in <i>M</i> isometric to the charged Nariai space.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"113 5","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5139927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Operator-valued Schatten spaces and quantum entropies 算符值Schatten空间与量子熵
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2023-08-29 DOI: 10.1007/s11005-023-01712-9
Salman Beigi, Milad M. Goodarzi
{"title":"Operator-valued Schatten spaces and quantum entropies","authors":"Salman Beigi,&nbsp;Milad M. Goodarzi","doi":"10.1007/s11005-023-01712-9","DOIUrl":"10.1007/s11005-023-01712-9","url":null,"abstract":"<div><p>Operator-valued Schatten spaces were introduced by G. Pisier as a noncommutative counterpart of vector-valued <span>(ell _p)</span>-spaces. This family of operator spaces forms an interpolation scale which makes it a powerful and convenient tool in a variety of applications. In particular, as the norms coming from this family naturally appear in the definition of certain entropic quantities in quantum information theory (QIT), one may apply Pisier’s theory to establish some features of those quantities. Nevertheless, it could be quite challenging to follow the proofs of the main results of this theory from the existing literature. In this article, we attempt to fill this gap by presenting the underlying concepts and ideas of Pisier’s theory in a self-contained way which we hope to be more accessible, especially for the QIT community at large. Furthermore, we describe some applications of this theory in QIT. In particular, we prove a new uniform continuity bound for the quantum conditional Rényi entropy.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"113 5","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-023-01712-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5112244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Renewal approach for the energy–momentum relation of the Fröhlich polaron Fröhlich极化子能量-动量关系的更新方法。
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2023-08-18 DOI: 10.1007/s11005-023-01711-w
Steffen Polzer
{"title":"Renewal approach for the energy–momentum relation of the Fröhlich polaron","authors":"Steffen Polzer","doi":"10.1007/s11005-023-01711-w","DOIUrl":"10.1007/s11005-023-01711-w","url":null,"abstract":"<div><p>We study the qualitative behaviour of the energy–momentum relation of the Fröhlich polaron at fixed coupling strength. Among other properties, we show that it is non-decreasing and that the correction to the quasi-particle energy is negative. We give a proof that the effective mass lies in <span>((1, infty ))</span> that does not need the validity of a central limit theorem for the path measure.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10435608/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10052115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Virial expansions for correlation functions in canonical ensemble 正则系综中相关函数的维里展开
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2023-07-18 DOI: 10.1007/s11005-023-01704-9
A. L. Rebenko
{"title":"Virial expansions for correlation functions in canonical ensemble","authors":"A. L. Rebenko","doi":"10.1007/s11005-023-01704-9","DOIUrl":"10.1007/s11005-023-01704-9","url":null,"abstract":"<div><p>The Kirkwood–Salzburg type equations are considered as nonlinear equations for the correlation functions of the canonical ensemble. Their solutions are built in the form of expansions in the powers of the density.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4722104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
Duality of orthogonal and symplectic random tensor models: general invariants 正交和辛随机张量模型的对偶性:一般不变量
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2023-07-12 DOI: 10.1007/s11005-023-01706-7
Hannes Keppler, Thomas Muller
{"title":"Duality of orthogonal and symplectic random tensor models: general invariants","authors":"Hannes Keppler,&nbsp;Thomas Muller","doi":"10.1007/s11005-023-01706-7","DOIUrl":"10.1007/s11005-023-01706-7","url":null,"abstract":"<div><p>In Gurau and Keppler 2022 (arxiv:2207.01993), a relation between orthogonal and symplectic tensor models with quartic interactions was proven. In this paper, we provide an alternative proof that extends to polynomial interactions of arbitrary order. We consider tensor models of order <i>D</i> with no symmetry under permutation of the indices that transform in the tensor product of <i>D</i> fundamental representations of <i>O</i>(<i>N</i>) and <i>Sp</i>(<i>N</i>). We explicitly show that the models obey the <i>N</i> to <span>(-N)</span> duality graph by graph in perturbation theory.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-023-01706-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4496870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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