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Born Geometry via Künneth Structures and Recursion Operators 通过k<s:1> nneth结构和递归算子生成几何
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05296-4
M. J. D. Hamilton, D. Kotschick, P. N. Pilatus
{"title":"Born Geometry via Künneth Structures and Recursion Operators","authors":"M. J. D. Hamilton,&nbsp;D. Kotschick,&nbsp;P. N. Pilatus","doi":"10.1007/s00220-025-05296-4","DOIUrl":"10.1007/s00220-025-05296-4","url":null,"abstract":"<div><p>We propose a simple definition of a Born geometry in the framework of Künneth geometry. While superficially different, this new definition is equivalent to the known definitions in terms of para-quaternionic or generalized geometries. We discuss integrability of Born structures and their associated connections. In particular we find that for integrable Born geometries the Born connection is obtained by a simple averaging under a conjugation from the Künneth connection. We also give examples of integrable Born geometries on nilmanifolds.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05296-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
GKZ Discriminant and Multiplicities 判别和多重性
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05266-w
Jesse Huang, Peng Zhou
{"title":"GKZ Discriminant and Multiplicities","authors":"Jesse Huang,&nbsp;Peng Zhou","doi":"10.1007/s00220-025-05266-w","DOIUrl":"10.1007/s00220-025-05266-w","url":null,"abstract":"<div><p>Let <span>(T=(mathbb {C}^*)^k)</span> act on <span>(V=mathbb {C}^N)</span> faithfully and preserving the volume form, i.e. <span>((mathbb {C}^*)^k hookrightarrow text {SL}(V))</span>. On the B-side, we have toric stacks <span>(Z_W)</span> (see Eq. 1.1) labelled by walls <i>W</i> in the GKZ fan, and <span>(Z_{/F})</span> labelled by faces of a polytope corresponding to minimal semi-orthogonal decomposition (SOD) components. The B-side multiplicity <span>(n^B_{W,F})</span>, well-defined by a result of Kite and Segal (Commun Math Phys 390:907-931, 2022), is the number of times <span>({{,textrm{Coh},}}(Z_{/F}))</span> appears in a complete SOD of <span>({{,textrm{Coh},}}(Z_W))</span>. On the A-side, we have the GKZ discriminant loci components <span>(nabla _F subset (mathbb {C}^*)^k)</span>, and its tropicalization <span>(nabla ^{trop}_{F} subset mathbb {R}^k)</span>. The A-side multiplicity <span>(n^A_{W, F})</span> is defined as the multiplicity of the tropical complex <span>(nabla ^{trop}_{F})</span> on wall <i>W</i>. We prove that <span>(n^A_{W,F} = n^B_{W,F })</span>, confirming a conjecture in Kite and Segal (Commun Math Phys 390:907-931, 2022) inspired by (Aspinwall et al. in Mirror symmetry and discriminants, http://arxiv.org/abs/1702.04661, 2017). Our proof is based on the result of Horja and Katzarkov (Discriminants and toric K-theory, http://arxiv.org/abs/2205.00903, 2022) and a lemma about B-side SOD multiplicity, which allows us to reduce to lower dimension just as in A-side (Gelfand et al. in Discriminants, resultants and multidimen sional determinants, Birkahuser, Boston, 1994) [Ch 11].</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Legendre Transformations of a Class of Generalized Frobenius Manifolds and the Associated Integrable Hierarchies 一类广义Frobenius流形及其可积层次的Legendre变换
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05289-3
Si-Qi Liu, Haonan Qu, Youjin Zhang
{"title":"Legendre Transformations of a Class of Generalized Frobenius Manifolds and the Associated Integrable Hierarchies","authors":"Si-Qi Liu,&nbsp;Haonan Qu,&nbsp;Youjin Zhang","doi":"10.1007/s00220-025-05289-3","DOIUrl":"10.1007/s00220-025-05289-3","url":null,"abstract":"<div><p>For two generalized Frobenius manifolds related by a Legendre-type transformation, we show that the associated integrable hierarchies of hydrodynamic type, which are called the Legendre-extended Principal Hierarchies, are related by a certain linear reciprocal transformation; we also show, under the semisimplicity condition, that the topological deformations of these Legendre-extended Principal Hierarchies are related by the same linear reciprocal transformation.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Quantitative Hydrodynamic Stability for Couette Flow on Unbounded Domains with Navier Boundary Conditions 具有Navier边界条件的无界区域上Couette流的定量水动力稳定性
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05306-5
Ryan Arbon, Jacob Bedrossian
{"title":"Quantitative Hydrodynamic Stability for Couette Flow on Unbounded Domains with Navier Boundary Conditions","authors":"Ryan Arbon,&nbsp;Jacob Bedrossian","doi":"10.1007/s00220-025-05306-5","DOIUrl":"10.1007/s00220-025-05306-5","url":null,"abstract":"<div><p>We prove a stability threshold theorem for 2D Navier–Stokes on three unbounded domains: the whole plane <span>(mathbb {R}times mathbb {R})</span>, the half plane <span>(mathbb {R}times [0,infty ))</span> with Navier boundary conditions, and the infinite channel <span>(mathbb {R}times [-1, 1])</span> with Navier boundary conditions. Starting with the Couette shear flow, we consider initial perturbations <span>(omega _{in})</span> which are of size <span>(nu ^{1/2}(1+ln (1/nu )^{1/2})^{-1})</span> in an anisotropic Sobolev space with an additional low frequency control condition for the planar cases. We then demonstrate that such perturbations exhibit inviscid damping of the velocity, as well as enhanced dissipation at <i>x</i>-frequencies <span>(|k| gg nu )</span> with decay time-scale <span>(O(nu ^{-1/3}|k|^{-2/3}))</span>. On the plane and half-plane, we show Taylor dispersion for <i>x</i>-frequencies <span>(|k| ll nu )</span> with decay time-scale <span>(O(nu |k|^{-2}))</span>, while on the channel we show low frequency dispersion for <span>(|k| ll nu )</span> with decay time-scale <span>(O(nu ^{-1}))</span>. Generalizing the work of Bedrossian et al. (Stability threshold of nearly-couette shear flows with Navier boundary conditions in 2d, 2311.00141, 2023) done on <span>(mathbb {T} times [-1,1])</span>, the key contribution of this paper is to perform new nonlinear computations at low frequencies with wave number <span>(|k| lesssim nu )</span> and at intermediate frequencies with wave number <span>(nu lesssim |k| le 1)</span>, and to provide the first enhanced dissipation result for a fully-nonlinear shear flow on an unbounded <i>x</i>-domain. Additionally, we demonstrate that the results of this paper apply equally to solutions of the perturbed <span>(beta )</span>-plane equations from atmospheric dynamics.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Local Statistics in Normal Matrix Models with Merging Singularity 具有合并奇异点的正态矩阵模型的局部统计量
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05316-3
Torben Krüger, Seung-Yeop Lee, Meng Yang
{"title":"Local Statistics in Normal Matrix Models with Merging Singularity","authors":"Torben Krüger,&nbsp;Seung-Yeop Lee,&nbsp;Meng Yang","doi":"10.1007/s00220-025-05316-3","DOIUrl":"10.1007/s00220-025-05316-3","url":null,"abstract":"<div><p>We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number <i>n</i> of particles tends to infinity we obtain the limiting local correlation kernel at the singularity, which is related to the parametrix of the Painlevé II equation. The two main tools are Riemann–Hilbert problems and the generalized Christoffel–Darboux identity. The correlation kernel exhibits a novel anisotropic scaling behavior, where the corresponding spacing scale of particles is <span>(n^{-1/3})</span> in the direction of merging and <span>(n^{-1/2})</span> in the perpendicular direction. In the vicinity at different distances to the merging singularity we also observe Ginibre bulk and edge statistics, as well as the sine-kernel and the erfc-type kernel (a.k.a. the Faddeeva plasma kernel).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Conformal Blocks on Smoothings via Mode Transition Algebras 经由模态转换代数的光滑上的共形块
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05237-1
Chiara Damiolini, Angela Gibney, Daniel Krashen
{"title":"Conformal Blocks on Smoothings via Mode Transition Algebras","authors":"Chiara Damiolini,&nbsp;Angela Gibney,&nbsp;Daniel Krashen","doi":"10.1007/s00220-025-05237-1","DOIUrl":"10.1007/s00220-025-05237-1","url":null,"abstract":"<div><p>Here we introduce a series of associative algebras attached to a vertex operator algebra <i>V</i> of CFT type, called mode transition algebras, and show they reflect both algebraic properties of <i>V</i> and geometric constructions on moduli of curves. Pointed and coordinatized curves, labeled by admissible <i>V</i>-modules, give rise to sheaves of coinvariants. We show that if the mode transition algebras admit multiplicative identities satisfying certain natural properties (called strong identity elements), these sheaves deform as wanted on families of curves with nodes. This provides new contexts in which coherent sheaves of coinvariants form vector bundles. We also show that mode transition algebras carry information about higher level Zhu algebras and generalized Verma modules. To illustrate, we explicitly describe the higher level Zhu algebras of the Heisenberg vertex operator algebra, proving a conjecture of Addabbo–Barron.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05237-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Universality of Outliers in Weakly Confined Coulomb-Type Systems 弱约束库仑型系统异常值的普遍性
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05293-7
Raphael Butez, David García-Zelada, Alon Nishry, Aron Wennman
{"title":"Universality of Outliers in Weakly Confined Coulomb-Type Systems","authors":"Raphael Butez,&nbsp;David García-Zelada,&nbsp;Alon Nishry,&nbsp;Aron Wennman","doi":"10.1007/s00220-025-05293-7","DOIUrl":"10.1007/s00220-025-05293-7","url":null,"abstract":"<div><p>This work concerns <i>weakly confined</i> particle systems in the plane, characterized by a large number of outliers away from a <i>droplet</i> where the bulk of the particles accumulate in the many-particle limit. We consider two main examples: determinantal Coulomb gases confined by a regular background, and a class of random polynomials. We observe that the limiting outlier process only depends on the <i>shape</i> of the uncharged region containing them, and the global net excess charge. In particular, for a determinantal Coulomb gas confined by a sufficiently regular background measure, the outliers in a simply connected uncharged region converge to the corresponding Bergman point process. For a finitely connected uncharged region <span>(Omega )</span>, we give an explicit description of the possible limiting outlier processes. Moreover, the outliers in different uncharged regions are asymptotically independent, even if the regions have common boundary points. The latter result is a manifestation of screening properties of the particle system.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Uniform Even Subgraph and Its Connection to Phase Transitions of Graphical Representations of the Ising Model Ising模型图形表示的一致偶子图及其与相变的联系
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05297-3
Ulrik Thinggaard Hansen, Boris Kjær, Frederik Ravn Klausen
{"title":"The Uniform Even Subgraph and Its Connection to Phase Transitions of Graphical Representations of the Ising Model","authors":"Ulrik Thinggaard Hansen,&nbsp;Boris Kjær,&nbsp;Frederik Ravn Klausen","doi":"10.1007/s00220-025-05297-3","DOIUrl":"10.1007/s00220-025-05297-3","url":null,"abstract":"<div><p>The uniform even subgraph is intimately related to the Ising model, the random-cluster model, the random current model, and the loop <span>(textrm{O})</span>(1) model. In this paper, we first prove that the uniform even subgraph of <span>(mathbb {Z}^d)</span> percolates for <span>(d ge 2)</span> using its characterisation as the Haar measure on the group of even graphs. We then tighten the result by showing that the loop <span>(textrm{O})</span>(1) model on <span>(mathbb {Z}^d)</span> percolates for <span>(d ge 2)</span> for edge-weights <i>x</i> lying in some interval <span>((1-varepsilon ,1])</span>. Finally, our main theorem is that the loop <span>(textrm{O})</span>(1) model and random current models corresponding to a supercritical Ising model are always at least critical, in the sense that their two-point correlation functions decay at most polynomially and the expected cluster sizes are infinite.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05297-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Perturbative Diagonalization and Spectral Gaps of Quasiperiodic Operators on (ell ^2(mathbb Z^d)) with Monotone Potentials (ell ^2(mathbb Z^d))上具有单调势的拟周期算子的微扰对角化和谱隙
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05280-y
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
{"title":"Perturbative Diagonalization and Spectral Gaps of Quasiperiodic Operators on (ell ^2(mathbb Z^d)) with Monotone Potentials","authors":"Ilya Kachkovskiy,&nbsp;Leonid Parnovski,&nbsp;Roman Shterenberg","doi":"10.1007/s00220-025-05280-y","DOIUrl":"10.1007/s00220-025-05280-y","url":null,"abstract":"<div><p>We obtain a perturbative proof of localization for quasiperiodic operators on <span>(ell ^2(mathbb Z^d))</span> with one-dimensional phase space and monotone sampling functions, in the regime of small hopping. The proof is based on an iterative scheme which can be considered as a local (in the energy and the phase) and convergent version of KAM-type diagonalization, whose result is a covariant family of uniformly localized eigenvalues and eigenvectors. We also prove that the spectra of such operators contain infinitely many gaps.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05280-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Affine (mathcal{W})-Algebras and Miura Maps from 3d (mathcal {N}text {=},4) Non-Abelian Quiver Gauge Theories 仿射(mathcal{W}) -代数和三维的Miura映射(mathcal {N}text {=},4)非阿贝尔颤振规范理论
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05277-7
Ioana Coman, Myungbo Shim, Masahito Yamazaki, Yehao Zhou
{"title":"Affine (mathcal{W})-Algebras and Miura Maps from 3d (mathcal {N}text {=},4) Non-Abelian Quiver Gauge Theories","authors":"Ioana Coman,&nbsp;Myungbo Shim,&nbsp;Masahito Yamazaki,&nbsp;Yehao Zhou","doi":"10.1007/s00220-025-05277-7","DOIUrl":"10.1007/s00220-025-05277-7","url":null,"abstract":"<div><p>We study Vertex Operator Algebras (VOAs) obtained from the H-twist of 3d <span>(mathcal {N}=4)</span> linear quiver gauge theories. We find that H-twisted VOAs can be regarded as the “chiralization” of the extended Higgs branch: many of the ingredients of the Higgs branch are naturally “uplifted” into the VOAs, while conversely the Higgs branch can be recovered as the associated variety of the VOA. We also discuss the connection of our VOA with affine <span>(mathcal {W})</span>-algebras. For example, we construct an explicit homomorphism from an affine <span>(mathcal {W})</span>-algebra <span>(mathcal{W}^{-n+1}(mathfrak {gl}_n,f_{min }))</span> into the H-twisted VOA for <span>(T^{[2,1^{n-2}]}_{[1^n]}[textrm{SU}(n)])</span> theories. Motivated by the relation with affine <span>(mathcal {W})</span>-algebras, we introduce a reduction procedure for the quiver diagram, and use this to give an algorithm to systematically construct novel free-field realizations for VOAs associated with general linear quivers.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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