Advances in Theoretical and Mathematical Physics最新文献

A QFT for non-semisimple TQFT 非半简 TQFT 的 QFT

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-08-19 DOI: 10.4310/atmp.2024.v28.n1.a4

Thomas Creutzig, Tudor Dimofte, Niklas Garner, Nathan Geer

{"title":"A QFT for non-semisimple TQFT","authors":"Thomas Creutzig, Tudor Dimofte, Niklas Garner, Nathan Geer","doi":"10.4310/atmp.2024.v28.n1.a4","DOIUrl":"https://doi.org/10.4310/atmp.2024.v28.n1.a4","url":null,"abstract":"$defTank{mathcal{T}^A_{n,k}}$$defUqsln{U_q(mathfrak{sl}_n)}$We construct a family of 3d quantum field theories $Tank$ that conjecturally provide a physical realization—and derived generalization—of non-semisimple mathematical TQFT’s based on the modules for the quantum group $Uqsln$ at an even root of unity $q = operatorname{exp}(i pi / k)$. The theories $Tank$ are defined as topological twists of certain 3d $mathcal{N=4}$ Chern–Simons-matter theories, which also admit string/M‑theory realizations. They may be thought of as $SU(n)_{k-n}$ Chern–Simons theories, coupled to a twisted $mathcal{N}=4$ matter sector (the source of non-semisimplicity). We show that $Tank$ admits holomorphic boundary conditions supporting two different logarithmic vertex operator algebras, one of which is an $mathfrak{sl}_n)$-type Feigin–Tipunin algebra; and we conjecture that these two vertex operator algebras are related by a novel logarithmic level-rank duality. (We perform detailed computations to support the conjecture.) We thus relate the category of line operators in $Tank$ to the derived category of modules for a boundary Feigin–Tipunin algebra, and—using a logarithmic Kazhdan–Lusztig-like correspondence that has been established for $n=2$ and expected for general $n$ — to the derived category of $Uqsln$ modules.We analyze many other key features of $Tank$ and match them from quantum-group and VOA perspectives, including deformations by flat $PGL(n,mathbb{C})$ connections, one-form symmetries, and indices of (derived) genus-$g$ state spaces.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Topological operators, noninvertible symmetries and decomposition 拓扑算子、不可逆对称和分解

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-08-14 DOI: 10.4310/atmp.2023.v27.n8.a2

Eric Sharpe

{"title":"Topological operators, noninvertible symmetries and decomposition","authors":"Eric Sharpe","doi":"10.4310/atmp.2023.v27.n8.a2","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n8.a2","url":null,"abstract":"In this paper we discuss noninvertible topological operators in the context of one-form symmetries and decomposition of twodimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete torsion. As one component of our analysis, we study the ring of dimension-zero operators in two-dimensional theories exhibiting decomposition. From a commutative algebra perspective, the rings are naturally associated to a finite number of points, one point for each universe in the decomposition. Each universe is canonically associated to a representation, which defines a projector, an idempotent in the ring of dimension-zero operators. We discuss how bulk Wilson lines act as defects bridging universes, and how Wilson lines on boundaries of two-dimensional theories decompose, and compute actions of projectors. We discuss one-form symmetries of the rings, and related properties. We also give general formulas for projection operators, which previously were computed on a case-by-case basis. Finally, we propose a characterization of noninvertible higher-form symmetries in this context in terms of representations. In that characterization, non-isomorphic universes appearing in decomposition are associated with noninvertible one-form symmetries.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Fuchsian ODEs as Seiberg dualities 作为塞伯格对偶性的福氏 ODEs

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-08-14 DOI: 10.4310/atmp.2023.v27.n8.a4

Sergio Cecotti

引用次数: 0

Energy spectrum of a constrained quantum particle and the Willmore energy of the constraining surface 受约束量子粒子的能谱和约束面的威尔摩尔能

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-08-14 DOI: 10.4310/atmp.2023.v27.n8.a3

Vicent Gimeno i Garcia, Steen Markvorsen

引用次数: 0

$K_2$ and quantum curves K_2$ 和量子曲线

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-08-14 DOI: 10.4310/atmp.2023.v27.n8.a1

Charles F. Doran, Matt Kerr, Soumya Sinha Babu

引用次数: 0

A QFT for non-semisimple TQFT 非半简 TQFT 的 QFT

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-07-29 DOI: 10.4310/atmp.2024.v28.n1.a3

Creutzig,Thomas, Dimofte,Tudor, Garner,Niklas, Geer,Nathan

{"title":"A QFT for non-semisimple TQFT","authors":"Creutzig,Thomas, Dimofte,Tudor, Garner,Niklas, Geer,Nathan","doi":"10.4310/atmp.2024.v28.n1.a3","DOIUrl":"https://doi.org/10.4310/atmp.2024.v28.n1.a3","url":null,"abstract":"We construct a family of 3d quantum field theories ${mathcal T}_{n,k}^A$ that conjecturally provide a physical realization --- and derived generalization --- of non-semisimple mathematical TQFT's based on the modules for the quantum group $U_q(mathfrak{sl}_n)$ at an even root of unity $q=text{exp}(ipi/k)$. The theories ${mathcal T}_{n,k}^A$ are defined as topological twists of certain 3d ${mathcal N}=4$ Chern-Simons-matter theories, which also admit string/M-theory realizations. They may be thought of as $SU(n)_{k-n}$ Chern-Simons theories, coupled to a twisted ${mathcal N}=4$ matter sector (the source of non-semisimplicity). We show that ${mathcal T}_{n,k}^A$ admits holomorphic boundary conditions supporting two different logarithmic vertex operator algebras, one of which is an $mathfrak{sl}_n$-type Feigin-Tipunin algebra; and we conjecture that these two vertex operator algebras are related by a novel logarithmic level-rank duality. (We perform detailed computations to support the conjecture.) We thus relate the category of line operators in ${mathcal T}_{n,k}^A$ to the derived category of modules for a boundary Feigin-Tipunin algebra, and --- using a logarithmic Kazhdan-Lusztig-like correspondence that has been established for $n=2$ and expected for general $n$ --- to the derived category of $U_q(mathfrak{sl}_n)$ modules. We analyze many other key features of ${mathcal T}_{n,k}^A$ and match them from quantum-group and VOA perspectives, including deformations by flat $PGL(n,mathbb C)$ connections, one-form symmetries, and indices of (derived) genus-$g$ state spaces.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Chiral topologically ordered states on a lattice from vertex operator algebras 从顶点算子代数看晶格上的手性拓扑有序态

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-07-29 DOI: 10.4310/atmp.2024.v28.n1.a1

Sopenko,Nikita

引用次数: 0

Jacobian Calabi--Yau 3-fold and charge completeness in six-dimensional theory 雅各布卡拉比--尤3折叠与六维理论中的电荷完备性

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-07-29 DOI: 10.4310/atmp.2024.v28.n1.a2

Kimura,Yusuke

引用次数: 0

Vafa-Witten theory: invariants, Floer homologies, Higgs bundles, a geometric Langlands correspondence, and categorification 瓦法-维滕理论：不变式、弗洛尔同调、希格斯束、几何朗兰兹对应和分类

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-07-16 DOI: 10.4310/atmp.2023.v27.n6.a3

Zhi-Cong Ong, Meng-Chwan Tan

{"title":"Vafa-Witten theory: invariants, Floer homologies, Higgs bundles, a geometric Langlands correspondence, and categorification","authors":"Zhi-Cong Ong, Meng-Chwan Tan","doi":"10.4310/atmp.2023.v27.n6.a3","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n6.a3","url":null,"abstract":"We revisit Vafa–Witten theory in the more general setting whereby the underlying moduli space is not that of instantons, but of the full Vafa–Witten equations. We physically derive (i) a novel Vafa–Witten four-manifold invariant associated with this moduli space, (ii) their relation to Gromov–Witten invariants, (iii) a novel Vafa–Witten Floer homology assigned to three-manifold boundaries, (iv) a novel Vafa–Witten Atiyah–Floer correspondence, (v) a proof and generalization of a conjecture by Abouzaid–Manolescu in $href{https://doi.org/10.4171/jems/994}{[2]}$ about the hypercohomology of a perverse sheaf of vanishing cycles, (vi) a Langlands duality of these invariants, Floer homologies and hypercohomology, and (vii) a quantum geometric Langlands correspondence with purely imaginary parameter that specializes to the classical correspondence in the zero-coupling limit, where Higgs bundles feature in (ii), (iv), (vi) and (vii). We also explain how these invariants and homologies will be categorified in the process, and discuss their higher categorification. We thereby relate differential and enumerative geometry, topology and geometric representation theory in mathematics, via a maximally-supersymmetric topological quantum field theory with electric-magnetic duality in physics.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Instanton counting and Donaldson–Thomas theory on toric Calabi–Yau four-orbifolds 环状 Calabi-Yau 四orbifold 上的瞬子计数和唐纳森-托马斯理论

IF 1.5 4区物理与天体物理

Advances in Theoretical and Mathematical Physics Pub Date : 2024-07-16 DOI: 10.4310/atmp.2023.v27.n6.a2

Richard J. Szabo, Michelangelo Tirelli

{"title":"Instanton counting and Donaldson–Thomas theory on toric Calabi–Yau four-orbifolds","authors":"Richard J. Szabo, Michelangelo Tirelli","doi":"10.4310/atmp.2023.v27.n6.a2","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n6.a2","url":null,"abstract":"We study rank $r$ cohomological Donaldson–Thomas theory on a toric Calabi–Yau orbifold of $mathbb{C}^4$ by a finite abelian subgroup $Gamma$ of $mathsf{SU}(4)$, from the perspective of instanton counting in cohomological gauge theory on a noncommutative crepant resolution of the quotient singularity. We describe the moduli space of noncommutative instantons on $mathbb{C}^4 / Gamma$ and its generalized ADHM parametrization. Using toric localization, we compute the orbifold instanton partition function as a combinatorial series over $r$-vectors of $Gamma$-coloured solid partitions. When the $Gamma$-action fixes an affine line in $mathbb{C}^4$, we exhibit the dimensional reduction to rank $r$ Donaldson–Thomas theory on the toric Kähler three-orbifold $mathbb{C}^3 / Gamma$. Based on this reduction and explicit calculations, we conjecture closed infinite product formulas, in terms of generalized MacMahon functions, for the instanton partition functions on the orbifolds $mathbb{C}^2 / mathbb{Z}_n times mathbb{C}^2$ and $mathbb{C}^3 / (mathbb{Z}_2 times mathbb{Z}_2) times mathbb{C}$, finding perfect agreement with new mathematical results of Cao, Kool and Monavari.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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