Letters in Mathematical Physics最新文献

{"title":"On intermediate exceptional series","authors":"Kimyeong Lee,&nbsp;Kaiwen Sun,&nbsp;Haowu Wang","doi":"10.1007/s11005-024-01861-5","DOIUrl":"10.1007/s11005-024-01861-5","url":null,"abstract":"<div><p>The Freudenthal–Tits magic square <span>(mathfrak {m}(mathbb {A}_1,mathbb {A}_2))</span> for <span>(mathbb {A}=mathbb {R},mathbb {C},mathbb {H},mathbb {O})</span> of semi-simple Lie algebras can be extended by including the sextonions <span>(mathbb {S})</span>. A series of non-reductive Lie algebras naturally appear in the new row associated with the sextonions, which we will call the <i>intermediate exceptional series</i>, with the largest one as the intermediate Lie algebra <span>(E_{7+1/2})</span> constructed by Landsberg–Manivel. We study various aspects of the intermediate vertex operator (super)algebras associated with the intermediate exceptional series, including rationality, coset constructions, irreducible modules, (super)characters and modular linear differential equations. For all <span>(mathfrak {g}_I)</span> belonging to the intermediate exceptional series, the intermediate VOA <span>(L_1(mathfrak {g}_I))</span> has characters of irreducible modules coinciding with those of the simple rational <span>(C_2)</span>-cofinite <i>W</i>-algebra <span>(W_{-h^vee /6}(mathfrak {g},f_theta ))</span> studied by Kawasetsu, with <span>(mathfrak {g} )</span> belonging to the Cvitanović–Deligne exceptional series. We propose some new intermediate VOA <span>(L_k(mathfrak {g}_I))</span> with integer level <i>k</i> and investigate their properties. For example, for the intermediate Lie algebra <span>(D_{6+1/2})</span> between <span>(D_6)</span> and <span>(E_7)</span> in the subexceptional series and also in Vogel’s projective plane, we find that the intermediate VOA <span>(L_2(D_{6+1/2}))</span> has a simple current extension to a SVOA with four irreducible Neveu–Schwarz modules, and the supercharacters can be realized by a fermionic Hecke operator on the <span>(N=1)</span> Virasoro minimal model <span>(L(c_{16,2},0))</span>. We also provide some (super) coset constructions such as <span>(L_2(E_7)/L_2(D_{6+1/2}))</span> and <span>(L_1(D_{6+1/2})^{otimes 2}!/L_2(D_{6+1/2}))</span>. In the end, we find that the theta blocks associated with the intermediate exceptional series produce some new holomorphic Jacobi forms of critical weight and lattice index.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01861-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413440","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}

{"title":"Defects and phase transitions to geometric phases of abelian GLSMs","authors":"Ilka Brunner,&nbsp;Lukas Krumpeck,&nbsp;Daniel Roggenkamp","doi":"10.1007/s11005-024-01852-6","DOIUrl":"10.1007/s11005-024-01852-6","url":null,"abstract":"<div><p>We consider gauged linear sigma models with gauge group <i>U</i>(1) that exhibit a geometric as well as a Landau–Ginzburg phase. We construct defects that implement the transport of D-branes from the Landau–Ginzburg phase to the geometric phase. Through their fusion with boundary conditions these defects in particular provide functors between the respective D-brane categories. The latter map (equivariant) matrix factorizations to coherent sheaves and can be formulated explicitly in terms of complexes of matrix factorizations.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01852-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413437","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}

{"title":"Quantum geodesic flows on graphs","authors":"Edwin Beggs,&nbsp;Shahn Majid","doi":"10.1007/s11005-024-01860-6","DOIUrl":"10.1007/s11005-024-01860-6","url":null,"abstract":"<div><p>We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the <i>n</i>-leg star graph for <span>(n=2,3,4)</span> and find the same phenomenon as recently found for the <span>(A_n)</span> Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here <span>(sqrt{n})</span>. We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line <span>(mathbb {Z})</span> with a general edge-symmetric metric.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01860-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269275","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}

{"title":"A cluster of results on amplituhedron tiles","authors":"Chaim Even-Zohar,&nbsp;Tsviqa Lakrec,&nbsp;Matteo Parisi,&nbsp;Melissa Sherman-Bennett,&nbsp;Ran Tessler,&nbsp;Lauren Williams","doi":"10.1007/s11005-024-01854-4","DOIUrl":"10.1007/s11005-024-01854-4","url":null,"abstract":"<div><p>The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in <span>(mathcal {N}=4)</span> super Yang–Mills theory. It generalizes <i>cyclic polytopes</i> and the <i>positive Grassmannian</i> and has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the <span>(m=4)</span> amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for <span>(text{ Gr}_{4,n})</span>. Secondly, we exhibit a tiling of the <span>(m=4)</span> amplituhedron which involves a tile which does not come from the BCFW recurrence—the <i>spurion</i> tile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for <span>(text{ Gr}_{4,n})</span>. This paper is a companion to our previous paper “Cluster algebras and tilings for the <span>(m=4)</span> amplituhedron.”</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01854-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219622","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}

{"title":"On an inequality of Lin, Kim and Hsieh and strong subadditivity","authors":"Eric A. Carlen,&nbsp;Michael P. Loss","doi":"10.1007/s11005-024-01857-1","DOIUrl":"10.1007/s11005-024-01857-1","url":null,"abstract":"<div><p>We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the von Neumann entropy.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01857-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219489","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}

{"title":"A general construction of family algebraic structures","authors":"Loïc Foissy,&nbsp;Dominique Manchon,&nbsp;Yuanyuan Zhang","doi":"10.1007/s11005-024-01851-7","DOIUrl":"10.1007/s11005-024-01851-7","url":null,"abstract":"<div><p>We give a general account of family algebras over a finitely presented linear operad. In a family algebra, each operation of arity <i>n</i> is replaced by a family of operations indexed by \u0000<span>(Omega ^n)</span>, where \u0000<span>(Omega )</span> is a set of parameters. We show that the operad, together with its presentation, naturally defines an algebraic structure on the set of parameters, which in turn is used in the description of the family version of the relations between operations. The examples of dendriform and duplicial family algebras (hence with two parameters) and operads are treated in detail, as well as the pre-Lie family case. Finally, free one-parameter duplicial family algebras are described, together with the extended duplicial semigroup structure on the set of parameters.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219488","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}

{"title":"Commutative Poisson algebras from deformations of noncommutative algebras","authors":"Alexander V. Mikhailov,&nbsp;Pol Vanhaecke","doi":"10.1007/s11005-024-01855-3","DOIUrl":"10.1007/s11005-024-01855-3","url":null,"abstract":"<div><p>It is well-known that a formal deformation of a commutative algebra <span>(mathcal {A})</span> leads to a Poisson bracket on <span>(mathcal {A})</span> and that the classical limit of a derivation on the deformation leads to a derivation on <span>(mathcal {A})</span>, which is Hamiltonian with respect to the Poisson bracket. In this paper we present a generalization of it for formal deformations of an arbitrary noncommutative algebra <span>(mathcal {A})</span>. The deformation leads in this case to a Poisson algebra structure on <span>(Pi (mathcal {A}){:}{=}Z(mathcal {A})times (mathcal {A}/Z(mathcal {A})))</span> and to the structure of a <span>(Pi (mathcal {A}))</span>-Poisson module on <span>(mathcal {A})</span>. The limiting derivations are then still derivations of <span>(mathcal {A})</span>, but with the Hamiltonian belong to <span>(Pi (mathcal {A}))</span>, rather than to <span>(mathcal {A})</span>. We illustrate our construction with several cases of formal deformations, coming from known quantum algebras, such as the ones associated with the nonabelian Volterra chains, Kontsevich integrable map, the quantum plane and the quantized Grassmann algebra.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01855-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219495","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}

{"title":"Existence and asymptotic behavior of nontrivial p-k-convex radial solutions for p-k-Hessian equations","authors":"Meiqiang Feng,&nbsp;Yichen Lu","doi":"10.1007/s11005-024-01858-0","DOIUrl":"10.1007/s11005-024-01858-0","url":null,"abstract":"<div><p>We study, via the eigenvalue theory of completely continuous operators, the existence and asymptotic behavior of nontrivial <i>p</i>-<i>k</i>-convex radial solutions for a <i>p</i>-<i>k</i>-Hessian equation. This is probably the first time that <i>p</i>-<i>k</i>-Hessian equations have been studied by employing this technique. Several new nonexistence conclusions are also derived in this paper.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219491","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}

{"title":"Mourre theory and spectral analysis of energy-momentum operators in relativistic quantum field theory","authors":"Janik Kruse","doi":"10.1007/s11005-024-01859-z","DOIUrl":"10.1007/s11005-024-01859-z","url":null,"abstract":"<div><p>A central task of theoretical physics is to analyse spectral properties of quantum mechanical observables. In this endeavour, Mourre’s conjugate operator method emerged as an effective tool in the spectral theory of Schrödinger operators. This paper introduces a novel class of examples from relativistic quantum field theory that are amenable to Mourre’s method. By assuming Lorentz covariance and the spectrum condition, we derive a limiting absorption principle for the energy-momentum operators and provide new proofs of the absolute continuity of the energy-momentum spectra. Moreover, under the assumption of dilation covariance, we show that the spectrum of the relativistic mass operator is purely absolutely continuous in <span>((0,infty ))</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01859-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219490","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}

{"title":"Support of the free measure for quantum field on fractal space-time","authors":"Tianjia Ni","doi":"10.1007/s11005-024-01853-5","DOIUrl":"10.1007/s11005-024-01853-5","url":null,"abstract":"<div><p>In constructive quantum theory, the free field is constructed based on a Gaussian measure on the space of tempered distributions. We generalize the classic results about support property of the Gaussian measure from Euclidean space-time to fractal space-time <span>(mathbb {R}times F)</span>. More precisely, we show that the set <span>((I-Delta _F)^{(d_s-1)/4+alpha }(1+| x| ^2)^{(d_H+1)/4+beta }L^2(mathbb {R}times F))</span> is of the Gaussian measure one if <span>(alpha &gt;0)</span> and <span>(beta &gt;0)</span>, while the set is of the Gaussian measure zero if <span>(alpha &gt;0)</span> and <span>(beta &lt;0)</span>. Here, <span>(Delta _F)</span> is the Laplacian on the underlying fractal space <i>F</i>, <span>(d_s)</span> is the spectral dimension of <span>(Delta _F)</span>, and <span>(d_H)</span> is the Hausdorff dimension of <i>F</i>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219492","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}