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Spectral Networks and Stability Conditions for Fukaya Categories with Coefficients 有系数的深谷分类的谱网络和稳定性条件
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05138-9
F. Haiden, L. Katzarkov, C. Simpson
{"title":"Spectral Networks and Stability Conditions for Fukaya Categories with Coefficients","authors":"F. Haiden,&nbsp;L. Katzarkov,&nbsp;C. Simpson","doi":"10.1007/s00220-024-05138-9","DOIUrl":"10.1007/s00220-024-05138-9","url":null,"abstract":"<div><p>Given a holomorphic family of Bridgeland stability conditions over a surface, we define a notion of spectral network which is an object in a Fukaya category of the surface with coefficients in a triangulated DG-category. These spectral networks are analogs of special Lagrangian submanifolds, combining a graph with additional algebraic data, and conjecturally correspond to semistable objects of a suitable stability condition on the Fukaya category with coefficients. They are closely related to the spectral networks of Gaiotto–Moore–Neitzke. One novelty of our approach is that we establish a general uniqueness results for spectral network representatives. We also verify the conjecture in the case when the surface is disk with six marked points on the boundary and the coefficients category is the derived category of representations of an <span>(A_2)</span> quiver. This example is related, via homological mirror symmetry, to the stacky quotient of an elliptic curve by the cyclic group of order six.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05138-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142430997","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
Generalised Entropy Accumulation 广义熵累积
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05121-4
Tony Metger, Omar Fawzi, David Sutter, Renato Renner
{"title":"Generalised Entropy Accumulation","authors":"Tony Metger,&nbsp;Omar Fawzi,&nbsp;David Sutter,&nbsp;Renato Renner","doi":"10.1007/s00220-024-05121-4","DOIUrl":"10.1007/s00220-024-05121-4","url":null,"abstract":"<div><p>Consider a sequential process in which each step outputs a system <span>(A_i)</span> and updates a side information register <i>E</i>. We prove that if this process satisfies a natural “non-signalling” condition between past outputs and future side information, the min-entropy of the outputs <span>(A_1, dots , A_n)</span> conditioned on the side information <i>E</i> at the end of the process can be bounded from below by a sum of von Neumann entropies associated with the individual steps. This is a generalisation of the entropy accumulation theorem (EAT) (Dupuis et al. in Commun Math Phys 379: 867–913, 2020), which deals with a more restrictive model of side information: there, past side information cannot be updated in subsequent rounds, and newly generated side information has to satisfy a Markov condition. Due to its more general model of side-information, our generalised EAT can be applied more easily and to a broader range of cryptographic protocols. As examples, we give the first multi-round security proof for blind randomness expansion and a simplified analysis of the E91 QKD protocol. The proof of our generalised EAT relies on a new variant of Uhlmann’s theorem and new chain rules for the Rényi divergence and entropy, which might be of independent interest.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05121-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431000","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
Noncommutative Logarithmic Sobolev Inequalities 非交换对数索波列夫不等式
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05145-w
Yong Jiao, Sijie Luo, Dmitriy Zanin, Dejian Zhou
{"title":"Noncommutative Logarithmic Sobolev Inequalities","authors":"Yong Jiao,&nbsp;Sijie Luo,&nbsp;Dmitriy Zanin,&nbsp;Dejian Zhou","doi":"10.1007/s00220-024-05145-w","DOIUrl":"10.1007/s00220-024-05145-w","url":null,"abstract":"<div><p>We show that the logarithmic Sobolev inequality holds for an arbitrary hypercontractive semigroup <span>({e^{-tP}}_{tge 0})</span> acting on a noncommutative probability space <span>(({mathcal {M}},tau ))</span>: </p><div><div><span>$$begin{aligned} Vert xVert _{L_p(log L)^{ps}({mathcal {M}})}le c_{p,s}Vert P^s(x)Vert _{L_p({mathcal {M}})},quad 1&lt;p&lt;infty , end{aligned}$$</span></div></div><p>for every mean zero <i>x</i> and <span>(0&lt;s&lt;infty )</span>. By selecting <span>(s=1/2)</span>, one can recover the <i>p</i>-logarithmic Sobolev inequality whenever the Riesz transform is bounded. Our inequality applies to numerous concrete cases, including Poisson semigroups for free groups, the Ornstein-Uhlenbeck semigroup for mixed <i>Q</i>-gaussian von Neumann algebras, the free product for Ornstein-Uhlenbeck semigroups etc. This provides a unified approach for functional analysis form of logarithmic Sobolev inequalities in general noncommutative setting.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431061","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
On the Superadditive Pressure for 1-Typical, One-Step, Matrix-Cocycle Potentials 论 1-典型、一步、矩阵-周期势的超加压力
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05118-z
Tom Rush
{"title":"On the Superadditive Pressure for 1-Typical, One-Step, Matrix-Cocycle Potentials","authors":"Tom Rush","doi":"10.1007/s00220-024-05118-z","DOIUrl":"10.1007/s00220-024-05118-z","url":null,"abstract":"<div><p>Let <span>((Sigma _T,sigma ))</span> be a subshift of finite type with primitive adjacency matrix <span>(T)</span>, <span>(psi :Sigma _T rightarrow mathbb {R})</span> a Hölder continuous potential, and <span>(mathcal {A}:Sigma _T rightarrow textrm{GL}_d(mathbb {R}))</span> a 1-typical, one-step cocycle. For <span>(t in mathbb {R})</span> consider the sequences of potentials <span>(Phi _t=(varphi _{t,n})_{n in mathbb {N}})</span> defined by </p><div><div><span>$$begin{aligned}varphi _{t,n}(x):=S_n psi (x) + tlog Vert mathcal {A}^n(x)Vert , , forall n in mathbb {N}.end{aligned}$$</span></div></div><p>Using the family of transfer operators defined in this setting by Park and Piraino, for all <span>(t&lt;0)</span> sufficiently close to 0 we prove the existence of Gibbs-type measures for the superadditive sequences of potentials <span>(Phi _t)</span>. This extends the results of the well-understood subadditive case where <span>(t ge 0)</span>. Prior to this, Gibbs-type measures were only known to exist for <span>(t&lt;0)</span> in the conformal, the reducible, the positive, or the dominated, planar settings, in which case they are Gibbs measures in the classical sense. We further prove that the topological pressure function <span>(t mapsto P_{textrm{top}}(Phi _t,sigma ))</span> is analytic in an open neighbourhood of 0 and has derivative given by the Lyapunov exponents of these Gibbs-type measures.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05118-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431062","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
Chaotic Properties of Billiards in Circular Polygons 圆多边形中台球的混沌特性
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05113-4
Andrew Clarke, Rafael Ramírez-Ros
{"title":"Chaotic Properties of Billiards in Circular Polygons","authors":"Andrew Clarke,&nbsp;Rafael Ramírez-Ros","doi":"10.1007/s00220-024-05113-4","DOIUrl":"10.1007/s00220-024-05113-4","url":null,"abstract":"<div><p>We study billiards in domains enclosed by circular polygons. These are closed <span>(C^1)</span> strictly convex curves formed by finitely many circular arcs. We prove the existence of a set in phase space, corresponding to generic sliding trajectories close enough to the boundary of the domain, in which the return billiard dynamics is semiconjugate to a transitive subshift on infinitely many symbols that contains the full <i>N</i>-shift as a topological factor for any <span>(N in {mathbb {N}})</span>, so it has infinite topological entropy. We prove the existence of uncountably many asymptotic generic sliding trajectories approaching the boundary with optimal uniform linear speed, give an explicit exponentially big (in <i>q</i>) lower bound on the number of <i>q</i>-periodic trajectories as <span>(q rightarrow infty )</span>, and present an unusual property of the length spectrum. Our proofs are entirely analytical.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431007","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
Comments on Global Symmetries and Anomalies of 5d SCFTs 关于 5d SCFT 全局对称性与反常现象的评论
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05139-8
Pietro Benetti Genolini, Luigi Tizzano
{"title":"Comments on Global Symmetries and Anomalies of 5d SCFTs","authors":"Pietro Benetti Genolini,&nbsp;Luigi Tizzano","doi":"10.1007/s00220-024-05139-8","DOIUrl":"10.1007/s00220-024-05139-8","url":null,"abstract":"<div><p>We study various aspects of global symmetries in five-dimensional superconformal field theories. Whenever a supersymmetry-preserving relevant deformation is available, the infrared gauge theory description might exhibit a finite order mixed ’t Hooft anomaly between a 1-form symmetry and the instantonic symmetry. This anomaly constrains the flavor symmetry group acting faithfully on the SCFT and the consistency of certain RG flows. As an additional example, we consider the instructive case of three-dimensional <span>(mathcal {N}=4)</span> SQED. Finally, we discuss the compatibility between conformal invariance and the presence of 1-form and 2-group global symmetries.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05139-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142430999","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
Dimension of Planar Non-conformal Attractors with Triangular Derivative Matrices 具有三角形衍生矩阵的平面非共形吸引子的维度
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05131-2
Balázs Bárány, Antti Käenmäki
{"title":"Dimension of Planar Non-conformal Attractors with Triangular Derivative Matrices","authors":"Balázs Bárány,&nbsp;Antti Käenmäki","doi":"10.1007/s00220-024-05131-2","DOIUrl":"10.1007/s00220-024-05131-2","url":null,"abstract":"<div><p>We study the dimension of the attractor and quasi-Bernoulli measures of parametrized families of iterated function systems of non-conformal and non-affine maps. We introduce a transversality condition under which, relying on a weak Ledrappier-Young formula, we show that the dimensions equal to the root of the subadditive pressure and the Lyapunov dimension, respectively, for almost every choice of parameters. We also exhibit concrete examples satisfying the transversality condition with respect to the translation parameters.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05131-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431005","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
Beyond the Holographic Entropy Cone via Cycle Flows 通过循环流超越全息熵锥
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05120-5
Temple He, Sergio Hernández-Cuenca, Cynthia Keeler
{"title":"Beyond the Holographic Entropy Cone via Cycle Flows","authors":"Temple He,&nbsp;Sergio Hernández-Cuenca,&nbsp;Cynthia Keeler","doi":"10.1007/s00220-024-05120-5","DOIUrl":"10.1007/s00220-024-05120-5","url":null,"abstract":"<div><p>Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of vertices, which corresponds to a subsystem, manifestly obeys purification symmetry. Furthermore, by restricting ourselves to a subclass of directed graphs, we prove that the maximum cycle flow obeys both subadditivity and strong subadditivity, thereby establishing it as a viable candidate for the entropy associated to the subsystem. Finally, we demonstrate how our model generalizes the entropy vectors obtainable via conventional flows in undirected graphs, as well as conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431060","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
Highest Weight Vectors in Plethysms, II 褶皱中重量最大的载体，II
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-07 DOI: 10.1007/s00220-024-05115-2
Kazufumi Kimoto, Soo Teck Lee
{"title":"Highest Weight Vectors in Plethysms, II","authors":"Kazufumi Kimoto,&nbsp;Soo Teck Lee","doi":"10.1007/s00220-024-05115-2","DOIUrl":"10.1007/s00220-024-05115-2","url":null,"abstract":"<div><p>For an irreducible polynomial representation <i>V</i> of the general linear group <span>(textrm{GL}_n(mathbb {C}))</span>, we realize its symmetric square <span>(S^2(V))</span> and its alternating square <span>(Lambda ^{hspace{-1.5pt}{2}}(V))</span> as spaces of polynomial functions. In the case when <i>V</i> is labeled by a Young diagram with at most 2 rows, we describe explicitly all the <span>(textrm{GL}_n(mathbb {C}))</span> highest weight vectors which occur in <span>(Votimes V)</span>, <span>(S^2(V))</span> and <span>(Lambda ^{hspace{-1.5pt}{2}}(V))</span> respectively. In particular, we obtain new description of the multiplicities in <span>(S^2(V))</span> and <span>(Lambda ^{hspace{-1.5pt}{2}}(V))</span>.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 10","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05115-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410416","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
Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion 具有弱分散性的分数非线性薛定谔方程的 Gibbs 动力学
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2024-10-07 DOI: 10.1007/s00220-024-05116-1
Rui Liang, Yuzhao Wang
{"title":"Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion","authors":"Rui Liang,&nbsp;Yuzhao Wang","doi":"10.1007/s00220-024-05116-1","DOIUrl":"10.1007/s00220-024-05116-1","url":null,"abstract":"<div><p>We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 10","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05116-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410446","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
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