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Quantization as a categorical equivalence 量化是一种分类等价
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-18 DOI: 10.1007/s11005-023-01765-w
Benjamin H. Feintzeig
{"title":"Quantization as a categorical equivalence","authors":"Benjamin H. Feintzeig","doi":"10.1007/s11005-023-01765-w","DOIUrl":"https://doi.org/10.1007/s11005-023-01765-w","url":null,"abstract":"<p>We demonstrate that, in certain cases, quantization and the classical limit provide functors that are “almost inverse” to each other. These functors map between categories of algebraic structures for classical and quantum physics, establishing a categorical equivalence.\u0000</p>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139507459","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}
引用次数: 0
Uniqueness of the extremal Schwarzschild de Sitter spacetime 极端施瓦兹柴尔德-德-西特时空的唯一性
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-18 DOI: 10.1007/s11005-023-01761-0
David Katona, James Lucietti
{"title":"Uniqueness of the extremal Schwarzschild de Sitter spacetime","authors":"David Katona, James Lucietti","doi":"10.1007/s11005-023-01761-0","DOIUrl":"https://doi.org/10.1007/s11005-023-01761-0","url":null,"abstract":"<p>We prove that any analytic vacuum spacetime with a positive cosmological constant in four and higher dimensions, that contains a static extremal Killing horizon with a maximally symmetric compact cross-section, must be locally isometric to either the extremal Schwarzschild de Sitter solution or its near-horizon geometry (the Nariai solution). In four-dimensions, this implies these solutions are the only analytic vacuum spacetimes that contain a static extremal horizon with compact cross-sections (up to identifications). We also consider the analogous uniqueness problem for the four-dimensional extremal hyperbolic Schwarzschild anti-de Sitter solution and show that it reduces to a spectral problem for the laplacian on compact hyperbolic surfaces, if a cohomological obstruction to the uniqueness of infinitesimal transverse deformations of the horizon is absent.</p>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139499075","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}
引用次数: 0
Reciprocity of the Chern–Simons invariants of 3-manifolds 3-manifolds的Chern-Simons不变式的互易性
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-11 DOI: 10.1007/s11005-023-01760-1
Takefumi Nosaka
{"title":"Reciprocity of the Chern–Simons invariants of 3-manifolds","authors":"Takefumi Nosaka","doi":"10.1007/s11005-023-01760-1","DOIUrl":"10.1007/s11005-023-01760-1","url":null,"abstract":"<div><p>We pose a reciprocity conjecture of the Chern–Simons invariants of 3-manifolds, and discuss some supporting evidence on the conjectures. Particularly, we show that the conjectures hold if Galois descent of a certain <span>(K_3)</span>-group is satisfied.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139419559","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}
引用次数: 0
Twisted formalism for 3d ({mathcal {N}}=4) theories 3d （{mathcal {N}}=4 ）理论的扭曲形式主义
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-10 DOI: 10.1007/s11005-023-01758-9
Niklas Garner
{"title":"Twisted formalism for 3d ({mathcal {N}}=4) theories","authors":"Niklas Garner","doi":"10.1007/s11005-023-01758-9","DOIUrl":"10.1007/s11005-023-01758-9","url":null,"abstract":"<div><p>We describe the topological <i>A</i> and <i>B</i> twists of 3d <span>({mathcal {N}}=4)</span> theories of hypermultiplets gauged by <span>({mathcal {N}}=4)</span> vector multiplets as certain deformations of the holomorphic–topological (<i>HT</i>) twist of those theories, utilizing the twisted superfields of Aganagic–Costello–Vafa–McNamara describing <i>HT</i>-twisted 3d <span>({mathcal {N}}=2)</span> theories. We rederive many known results from this perspective, including state spaces on Riemann surfaces, deformations induced by flavor symmetries, the boundary VOAs of Costello–Gaiotto, and the category of line operators as proposed by Costello–Dimofte–Gaiotto–Hilburn–Yoo. Along the way, we show how the secondary product of local operators in the holomorphic–topological twist is related to the secondary product in the fully topological twist.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139419550","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}
引用次数: 0
Equivariant localization and holography 等价定位和全息学
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-08 DOI: 10.1007/s11005-023-01752-1
Dario Martelli, Alberto Zaffaroni
{"title":"Equivariant localization and holography","authors":"Dario Martelli,&nbsp;Alberto Zaffaroni","doi":"10.1007/s11005-023-01752-1","DOIUrl":"10.1007/s11005-023-01752-1","url":null,"abstract":"<div><p>We discuss the theory of equivariant localization focussing on applications relevant for holography. We consider geometries comprising compact and non-compact toric orbifolds, as well as more general non-compact toric Calabi–Yau singularities. A key object in our constructions is the <i>equivariant volume</i>, for which we describe two methods of evaluation: the Berline–Vergne fixed point formula and the Molien–Weyl formula, supplemented by the Jeffrey–Kirwan prescription. We present two applications in supersymmetric field theories. Firstly, we describe a method for integrating the anomaly polynomial of SCFTs on compact toric orbifolds. Secondly, we discuss equivariant orbifold indices that are expected to play a key role in the computation of supersymmetric partition functions. In the context of supergravity, we propose that the equivariant volume can be used to characterize universally the geometry of a large class of supersymmetric solutions. As an illustration, we employ equivariant localization to prove the factorization in gravitational blocks of various supergravity free energies, recovering previous results as well as obtaining generalizations.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-023-01752-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139399902","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}
引用次数: 0
On intermediate Lie algebra (E_{7+1/2}) 关于中间列代数 $$E_{7+1/2}$$
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-06 DOI: 10.1007/s11005-023-01762-z
Kimyeong Lee, Kaiwen Sun, Haowu Wang
{"title":"On intermediate Lie algebra (E_{7+1/2})","authors":"Kimyeong Lee,&nbsp;Kaiwen Sun,&nbsp;Haowu Wang","doi":"10.1007/s11005-023-01762-z","DOIUrl":"10.1007/s11005-023-01762-z","url":null,"abstract":"<div><p><span>(E_{7+1/2})</span> is an intermediate Lie algebra filling a hole between <span>(E_7)</span> and <span>(E_8)</span> in the Deligne–Cvitanović exceptional series. It was found independently by Mathur, Muhki, Sen in the classification of 2d RCFTs via modular linear differential equations (MLDE) and by Deligne, Cohen, de Man in representation theory. In this paper we propose some new vertex operator algebras (VOA) associated with <span>(E_{7+1/2})</span> and give some useful information at small levels. We conjecture that the affine VOA <span>((E_{7+1/2})_k)</span> is rational if and only if the level <i>k</i> is at most 5, and provide some evidence from the viewpoint of MLDE. We propose a conjectural Weyl dimension formula for infinitely many irreducible representations of <span>(E_{7+1/2})</span>, which generates almost all irreducible representations of <span>(E_{7+1/2})</span> with level <span>(kle 4)</span>. More concretely, we propose the affine VOA <span>(E_{7+1/2})</span> at level 2 and the rank-two instanton VOA associated with <span>(E_{7+1/2})</span>. We compute the VOA characters and provide some coset constructions. These generalize the previous works of Kawasetsu for affine VOA <span>(E_{7+1/2})</span> at level 1 and of Arakawa–Kawasetsu at level <span>(-5)</span>. We then predict the conformal weights of affine VOA <span>(E_{7+1/2})</span> at level 3, 4, 5.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-023-01762-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375583","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}
引用次数: 0
Almost multiplicity free subgroups of compact Lie groups and polynomial integrability of sub-Riemannian geodesic flows 紧凑李群的几乎无多重性子群与亚黎曼大地流的多项式可积分性
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-06 DOI: 10.1007/s11005-023-01757-w
Božidar Jovanović, Tijana Šukilović, Srdjan Vukmirović
{"title":"Almost multiplicity free subgroups of compact Lie groups and polynomial integrability of sub-Riemannian geodesic flows","authors":"Božidar Jovanović,&nbsp;Tijana Šukilović,&nbsp;Srdjan Vukmirović","doi":"10.1007/s11005-023-01757-w","DOIUrl":"10.1007/s11005-023-01757-w","url":null,"abstract":"<div><p>We classify almost multiplicity free subgroups <i>K</i> of compact simple Lie groups <i>G</i>. The problem is related to the integrability of Riemannian and sub-Riemannian geodesic flows of left-invariant metrics defined by a specific extension of integrable systems from <span>(T^*K)</span> to <span>(T^*G)</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375447","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}
引用次数: 0
A Wilson line realization of quantum groups 量子群的威尔逊线实现
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-05 DOI: 10.1007/s11005-023-01756-x
Nanna Aamand, Dani Kaufman
{"title":"A Wilson line realization of quantum groups","authors":"Nanna Aamand,&nbsp;Dani Kaufman","doi":"10.1007/s11005-023-01756-x","DOIUrl":"10.1007/s11005-023-01756-x","url":null,"abstract":"<div><p>We study Wilson line operators in three-dimensional Chern–Simons theory on a manifold with boundaries and prove to leading order, through a direct calculation of Feynman integrals, that the merging of parallel Wilson lines reproduces the coproduct on the quantum group <span>(U_hbar ({mathfrak {g}}))</span>. We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-023-01756-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102130","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}
引用次数: 0
From projective representations to pentagonal cohomology via quantization 通过量子化从投影表示到五角同调
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-04 DOI: 10.1007/s11005-023-01754-z
Victor Gayral, Valentin Marie
{"title":"From projective representations to pentagonal cohomology via quantization","authors":"Victor Gayral,&nbsp;Valentin Marie","doi":"10.1007/s11005-023-01754-z","DOIUrl":"10.1007/s11005-023-01754-z","url":null,"abstract":"<div><p>Given a locally compact group <span>(G=Q &lt; imes V)</span> such that <i>V</i> is Abelian and such that the action of <i>Q</i> on the Pontryagin dual <span>({hat{V}})</span> has a free orbit of full measure, we construct a family of unitary dual 2-cocycles <span>(Omega _omega )</span> (aka non-formal Drinfel’d twists) whose equivalence classes <span>([Omega _omega ]in H^2({hat{G}},{mathbb {T}}))</span> are parametrized by cohomology classes <span>([omega ]in H^2(Q,{mathbb {T}}))</span>. We prove that the associated locally compact quantum groups are isomorphic to cocycle bicrossed product quantum groups associated with a pair of subgroups of the dual semidirect product <span>(Q &lt; imes {hat{V}})</span>, both isomorphic to <i>Q</i>, and to a pentagonal cocycle <span>(Theta _omega )</span> explicitly given in terms of the group cocycle <span>(omega )</span>.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094236","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}
引用次数: 0
Kostant’s problem for Whittaker modules Whittaker 模块的 Kostant 问题
IF 1.2 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-01-03 DOI: 10.1007/s11005-023-01759-8
Chih-Whi Chen
{"title":"Kostant’s problem for Whittaker modules","authors":"Chih-Whi Chen","doi":"10.1007/s11005-023-01759-8","DOIUrl":"10.1007/s11005-023-01759-8","url":null,"abstract":"<div><p>We study the classical problem of Kostant for Whittaker modules over Lie algebras and Lie superalgebras. We give a sufficient condition for a positive answer to Kostant’s problem for the standard Whittaker modules over reductive Lie algebras. Under the same condition, the positivity of the answer for simple Whittaker modules is reduced to that for simple highest weight modules. We develop several reduction results to reduce the Kostant’s problem for standard and simple Whittaker modules over a type I Lie superalgebra to that for the corresponding Whittaker modules over the even part of this Lie superalgebra.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139090591","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}
引用次数: 0
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