Letters in Mathematical Physics最新文献

{"title":"On B-type family of Dubrovin–Frobenius manifolds and their integrable systems","authors":"Alexey Basalaev","doi":"10.1007/s11005-024-01867-z","DOIUrl":"10.1007/s11005-024-01867-z","url":null,"abstract":"<div><p>According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin–Frobenius manifold indexed by (<i>k</i>, <i>l</i>) can be recovered by the <span>((k+r,l+r))</span> Dubrovin–Frobenius manifold.Continuing the program of Basalaev et al. (J Phys A: Math Theor 54:115201, 2021) we associate an infinite system of commuting PDEs to these Dubrovin–Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431053","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":"Hadamard property of the Unruh state for massless fermions on Kerr spacetime: the large a case","authors":"Dietrich Häfner,&nbsp;Christiane Klein","doi":"10.1007/s11005-024-01862-4","DOIUrl":"10.1007/s11005-024-01862-4","url":null,"abstract":"<div><p>In Gérard et al. (Ann Sci Ecole Norm Sup 56:127–196, 2023), the Unruh state for massless fermions on a Kerr spacetime was constructed and the authors showed its Hadmard property in the case of very slowly rotating black holes <span>({left| a right| }ll M)</span>. In this note, we extend this result to the full non extreme case <span>({left| a right| }&lt;M)</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411151","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":"On absolutely continuous spectrum for one-channel unitary operators","authors":"Olivier Bourget,&nbsp;Gregorio Moreno,&nbsp;Christian Sadel,&nbsp;Amal Taarabt","doi":"10.1007/s11005-024-01866-0","DOIUrl":"10.1007/s11005-024-01866-0","url":null,"abstract":"<div><p>In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona’s formula and deduce criteria for absolutely continuous spectrum which we apply to random Hilbert Schmidt perturbations of periodic scattering zippers.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411179","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":"Young wall models for the level 1 highest weight and Fock space crystals of (U_q(E_6^{(2)})) and (U_q(F_4^{(1)}))","authors":"Shaolong Han,&nbsp;Yuanfeng Jin,&nbsp;Seok-Jin Kang,&nbsp;Duncan Laurie","doi":"10.1007/s11005-024-01845-5","DOIUrl":"10.1007/s11005-024-01845-5","url":null,"abstract":"<div><p>In this paper, we construct Young wall models for the level 1 highest weight and Fock space crystals of quantum affine algebras in types <span>(E_6^{(2)})</span> and <span>(F_4^{(1)})</span>. Our starting point in each case is a combinatorial realization for a certain level 1 perfect crystal in terms of Young columns. Then, using energy functions and affine energy functions we define the notions of reduced and proper Young walls, which model the highest weight and Fock space crystals, respectively.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415284","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":"Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems","authors":"Houssam Abdul-Rahman,&nbsp;Robert Sims,&nbsp;Günter Stolz","doi":"10.1007/s11005-024-01863-3","DOIUrl":"10.1007/s11005-024-01863-3","url":null,"abstract":"<div><p>We provide an analytic method for estimating the entanglement of the non-Gaussian energy eigenstates of disordered harmonic oscillator systems. We invoke the explicit formulas of the eigenstates of the oscillator systems to establish bounds for their <span>(epsilon )</span>-Rényi entanglement entropy <span>(epsilon in (0,1))</span>. Our methods result in a logarithmically corrected area law for the entanglement of eigenstates, corresponding to one excitation, of the disordered harmonic oscillator systems.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413663","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":"Non-stationary difference equation for q-Virasoro conformal blocks","authors":"Sh. Shakirov","doi":"10.1007/s11005-024-01856-2","DOIUrl":"10.1007/s11005-024-01856-2","url":null,"abstract":"<div><p>Conformal blocks of <i>q</i>, <i>t</i>-deformed Virasoro and <span>({mathcal {W}})</span>-algebras are important special functions in representation theory with applications in geometry and physics. In the Nekrasov–Shatashvili limit <span>(t rightarrow 1)</span>, whenever one of the representations is degenerate then conformal block satisfies a difference equation with respect to the coordinate associated with that degenerate representation. This is a stationary Schrodinger equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generic <span>(t ne 1)</span> is a non-stationary Schrodinger equation where <i>t</i> parametrizes shift in time. In this paper we make the non-stationary equation explicit for the <i>q</i>, <i>t</i>-Virasoro block with one degenerate and four generic Verma modules and prove it when three modules out of five are degenerate, using occasional relation to Macdonald polynomials.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413695","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":"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}