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Existence of Approximately Macroscopically Unique States 近似宏观唯一态的存在性
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-16 DOI: 10.1007/s00220-024-05218-w
Huaxin Lin
{"title":"Existence of Approximately Macroscopically Unique States","authors":"Huaxin Lin","doi":"10.1007/s00220-024-05218-w","DOIUrl":"10.1007/s00220-024-05218-w","url":null,"abstract":"<div><p>Let <i>H</i> be an infinite dimensional separable Hilbert space and <i>B</i>(<i>H</i>) the <span>(C^*)</span>-algebra  of bounded operators on <i>H</i>. Suppose that <span>(T_1,T_2,..., T_n)</span> are self-adjoint operators in <i>B</i>(<i>H</i>). We show that, if commutators <span>([T_i, T_j])</span> are sufficiently small in norm, then “Approximately Macroscopically Unique\" states always exist for any values in a synthetic spectrum of the <i>n</i>-tuple of self-adjoint operators. This is achieved under the circumstance for which the <i>n</i>-tuple may not be approximated by commuting ones. This answers a question proposed by David Mumford for measurements in quantum theory. If commutators are not small in norm but small modulo compact operators, then “Approximate Macroscopic Uniqueness\" states also exist.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994800","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
Large N von Neumann Algebras and the Renormalization of Newton’s Constant 大N冯诺依曼代数和牛顿常数的重整化
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-16 DOI: 10.1007/s00220-024-05192-3
Elliott Gesteau
{"title":"Large N von Neumann Algebras and the Renormalization of Newton’s Constant","authors":"Elliott Gesteau","doi":"10.1007/s00220-024-05192-3","DOIUrl":"10.1007/s00220-024-05192-3","url":null,"abstract":"<div><p>I derive a family of Ryu–Takayanagi formulae that are valid in the large <i>N</i> limit of holographic quantum error-correcting codes, and parameterized by a choice of UV cutoff in the bulk. The bulk entropy terms are matched with a family of von Neumann factors nested inside the large <i>N</i> von Neumann algebra describing the bulk effective field theory. These factors are mapped onto one another by a family of conditional expectations, which are interpreted as a renormalization group flow for the code subspace. Under this flow, I show that the renormalizations of the area term and the bulk entropy term exactly compensate each other. This result provides a concrete realization of the ER=EPR paradigm, as well as an explicit proof of a conjecture due to Susskind and Uglum.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994801","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
Quantum Broadcast Channel Simulation via Multipartite Convex Splitting 基于多部凸分裂的量子广播信道仿真
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-16 DOI: 10.1007/s00220-024-05191-4
Mario Berta, Hao-Chung Cheng, Li Gao
{"title":"Quantum Broadcast Channel Simulation via Multipartite Convex Splitting","authors":"Mario Berta,&nbsp;Hao-Chung Cheng,&nbsp;Li Gao","doi":"10.1007/s00220-024-05191-4","DOIUrl":"10.1007/s00220-024-05191-4","url":null,"abstract":"<div><p>We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel’s multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched Rényi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05191-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994802","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
On Some Simple Orbifold Affine VOAs at Non-admissible Level Arising from Rank One 4D SCFTs 一类四维scft产生的非容许能级的简单轨道仿射VOAs
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-11 DOI: 10.1007/s00220-024-05196-z
Tomoyuki Arakawa, Xuanzhong Dai, Justine Fasquel, Bohan Li, Anne Moreau
{"title":"On Some Simple Orbifold Affine VOAs at Non-admissible Level Arising from Rank One 4D SCFTs","authors":"Tomoyuki Arakawa,&nbsp;Xuanzhong Dai,&nbsp;Justine Fasquel,&nbsp;Bohan Li,&nbsp;Anne Moreau","doi":"10.1007/s00220-024-05196-z","DOIUrl":"10.1007/s00220-024-05196-z","url":null,"abstract":"<div><p>We study the representations of some simple affine vertex algebras at non-admissible level arising from rank one 4D SCFTs. In particular, we classify the irreducible highest weight modules of <span>(L_{-2}(G_2))</span> and <span>(L_{-2}(B_3))</span>. It is known by the works of Adamović and Perše that these vertex algebras can be conformally embedded into <span>(L_{-2}(D_4))</span>. We also compute the associated variety of <span>(L_{-2}(G_2))</span>, and show that it is the orbifold of the associated variety of <span>(L_{-2}(D_4))</span> by the symmetric group of degree 3 which is the Dynkin diagram automorphism group of <span>(D_4)</span>. This provides a new interesting example of associated variety satisfying a number of conjectures in the context of orbifold vertex algebras.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962955","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
B-Twisted Gaiotto–Witten Theory and Topological Quantum Field Theory b -扭曲Gaiotto-Witten理论与拓扑量子场论
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-11 DOI: 10.1007/s00220-024-05211-3
Niklas Garner, Nathan Geer, Matthew B. Young
{"title":"B-Twisted Gaiotto–Witten Theory and Topological Quantum Field Theory","authors":"Niklas Garner,&nbsp;Nathan Geer,&nbsp;Matthew B. Young","doi":"10.1007/s00220-024-05211-3","DOIUrl":"10.1007/s00220-024-05211-3","url":null,"abstract":"<div><p>We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto–Witten theory with linear matter. Our constructions are based on relative modular structures on the category of weight modules over an unrolled quantization of a Lie superalgebra. The Lie superalgebra, originally defined by Gaiotto and Witten, is associated to a complex symplectic representation of a metric abelian Lie algebra. The physical theories we model admit alternative realizations as Chern–Simons–Rozansky–Witten theories and supergroup Chern–Simons theories and include as particular examples global forms of <span>(mathfrak {gl}(1 vert 1))</span>-Chern–Simons theory and toral Chern–Simons theory. Fundamental to our approach is the systematic incorporation of non-genuine line operators which source flat connections for the topological flavour symmetry of the theory.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963045","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
Magnetic Flatness and E. Hopf’s Theorem for Magnetic Systems 磁系统的磁平坦度与E. Hopf定理
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-11 DOI: 10.1007/s00220-024-05166-5
Valerio Assenza, James Marshall Reber, Ivo Terek
{"title":"Magnetic Flatness and E. Hopf’s Theorem for Magnetic Systems","authors":"Valerio Assenza,&nbsp;James Marshall Reber,&nbsp;Ivo Terek","doi":"10.1007/s00220-024-05166-5","DOIUrl":"10.1007/s00220-024-05166-5","url":null,"abstract":"<div><p>Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf’s theorem to the setting of magnetic systems. Namely, we prove that if the magnetic flow on the <i>s</i>-sphere bundle is without conjugate points, then the total magnetic curvature is non-positive, and vanishes if and only if the magnetic system is magnetically flat. We then prove that magnetic flatness is a rigid condition, in the sense that it only occurs when either the magnetic form is trivial and the metric is flat, or when the magnetic system is Kähler, the metric has constant negative sectional holomorphic curvature, and <i>s</i> equals the Mañé critical value.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05166-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963110","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
First Passage Percolation, Local Uniqueness for Interlacements and Capacity of Random Walk 第一通道渗透、交错的局部唯一性与随机游走容量
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-11 DOI: 10.1007/s00220-024-05195-0
Alexis Prévost
{"title":"First Passage Percolation, Local Uniqueness for Interlacements and Capacity of Random Walk","authors":"Alexis Prévost","doi":"10.1007/s00220-024-05195-0","DOIUrl":"10.1007/s00220-024-05195-0","url":null,"abstract":"<div><p>The study of first passage percolation (FPP) for the random interlacements model has been initiated in Andres and Prévost (Ann Appl Probab 34(2):1846–1895), where it is shown that on <span>(mathbb {Z}^d)</span>, <span>(dge 3)</span>, the FPP distance is comparable to the graph distance with high probability. In this article, we give an asymptotically sharp lower bound on this last probability, which additionally holds on a large class of transient graphs with polynomial volume growth and polynomial decay of the Green function. When considering the interlacement set in the low-intensity regime, the previous bound is in fact valid throughout the near-critical phase. In low dimension, we also present two applications of this FPP result: sharp large deviation bounds on local uniqueness of random interlacements, and on the capacity of a random walk in a ball.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05195-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962948","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
Six-dimensional Supermultiplets from Bundles on Projective Spaces 射影空间上束的六维超重态
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-11 DOI: 10.1007/s00220-024-05176-3
Fabian Hahner, Simone Noja, Ingmar Saberi, Johannes Walcher
{"title":"Six-dimensional Supermultiplets from Bundles on Projective Spaces","authors":"Fabian Hahner,&nbsp;Simone Noja,&nbsp;Ingmar Saberi,&nbsp;Johannes Walcher","doi":"10.1007/s00220-024-05176-3","DOIUrl":"10.1007/s00220-024-05176-3","url":null,"abstract":"<div><p>The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to <span>(mathbb {P}^1 times mathbb {P}^3)</span>. We use this fact, together with the pure spinor superfield formalism, to study supermultiplets in six dimensions, starting from vector bundles on projective spaces. We classify all multiplets whose derived invariants for the supertranslation algebra form a line bundle over the nilpotence variety; one can think of such multiplets as being those whose holomorphic twists have rank one over Dolbeault forms on spacetime. In addition, we explicitly construct multiplets associated to natural higher-rank equivariant vector bundles, including the tangent and normal bundles as well as their duals. Among the multiplets constructed are the vector multiplet and hypermultiplet, the family of <span>({mathcal {O}}(n))</span>-multiplets, and the supergravity and gravitino multiplets. Along the way, we tackle various theoretical problems within the pure spinor superfield formalism. In particular, we give some general discussion about the relation of the projective nilpotence variety to multiplets and prove general results on short exact sequences and dualities of sheaves in the context of the pure spinor superfield formalism.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05176-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962952","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
Lieb–Thirring Inequality for the 2D Pauli Operator 二维泡利算子的Lieb-Thirring不等式
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-11 DOI: 10.1007/s00220-024-05177-2
Rupert L. Frank, Hynek Kovařík
{"title":"Lieb–Thirring Inequality for the 2D Pauli Operator","authors":"Rupert L. Frank,&nbsp;Hynek Kovařík","doi":"10.1007/s00220-024-05177-2","DOIUrl":"10.1007/s00220-024-05177-2","url":null,"abstract":"<div><p>By the Aharonov–Casher theorem, the Pauli operator <i>P</i> has no zero eigenvalue when the normalized magnetic flux <span>(alpha )</span> satisfies <span>(|alpha |&lt;1)</span>, but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the <span>(gamma )</span>-th moment of the eigenvalues of <span>(P+V)</span> is valid under the optimal restrictions <span>(gamma ge |alpha |)</span> and <span>(gamma &gt;0)</span>. Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order <span>(gamma ge 1)</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05177-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962954","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
Conformal Field Theory, Solitons, and Elliptic Calogero–Sutherland Models 共形场论，孤子和椭圆Calogero-Sutherland模型
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-01-11 DOI: 10.1007/s00220-024-05188-z
Bjorn K. Berntson, Edwin Langmann, Jonatan Lenells
{"title":"Conformal Field Theory, Solitons, and Elliptic Calogero–Sutherland Models","authors":"Bjorn K. Berntson,&nbsp;Edwin Langmann,&nbsp;Jonatan Lenells","doi":"10.1007/s00220-024-05188-z","DOIUrl":"10.1007/s00220-024-05188-z","url":null,"abstract":"<div><p>We construct a non-chiral conformal field theory (CFT) on the torus that accommodates a second quantization of the elliptic Calogero–Sutherland (eCS) model. We show that the CFT operator that provides this second quantization defines, at the same time, a quantum version of a soliton equation called the non-chiral intermediate long-wave (ncILW) equation. We also show that this CFT operator is a second quantization of a generalized eCS model which can describe arbitrary numbers of four different kinds of particles; we propose that these particles can be identified with solitons of the quantum ncILW equation.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05188-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962949","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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