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Two-dimensional perturbative scalar QFT and Atiyah–Segal gluing 二维微扰标量QFT与Atiyah-Segal胶合
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-12-24 DOI: 10.4310/ATMP.2021.v25.n7.a5
Santosh Kandel, P. Mnev, K. Wernli
{"title":"Two-dimensional perturbative scalar QFT and Atiyah–Segal gluing","authors":"Santosh Kandel, P. Mnev, K. Wernli","doi":"10.4310/ATMP.2021.v25.n7.a5","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n7.a5","url":null,"abstract":"We study the perturbative quantization of 2-dimensional massive scalar field theory with polynomial (or power series) potential on manifolds with boundary. We prove that it fits into the functorial quantum field theory framework of Atiyah-Segal. In particular, we prove that the perturbative partition function defined in terms of integrals over configuration spaces of points on the surface satisfies an Atiyah-Segal type gluing formula. Tadpoles (short loops) behave nontrivially under gluing and play a crucial role in the result.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"19 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87149717","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: 2
Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams 微分上同伦意味着通过构形空间和弦图相交膜观测
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-12-22 DOI: 10.4310/atmp.2022.v26.n4.a4
H. Sati, U. Schreiber
{"title":"Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams","authors":"H. Sati, U. Schreiber","doi":"10.4310/atmp.2022.v26.n4.a4","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n4.a4","url":null,"abstract":"We introduce a differential refinement of Cohomotopy cohomology theory, defined on Penrose diagram spacetimes, whose cocycle spaces are unordered configuration spaces of points. First we prove that brane charge quantization in this differential 4-Cohomotopy theory implies intersecting p/(p+2)-brane moduli given by ordered configurations of points in the transversal 3-space. Then we show that the higher (co-)observables on these brane moduli, conceived as the (co-)homology of the Cohomotopy cocycle space, are given by weight systems on horizontal chord diagrams and reflect a multitude of effects expected in the microscopic quantum theory of Dp/D(p+2)-brane intersections: condensation to stacks of coincident branes and their Chan-Paton factors, BMN matrix model and fuzzy funnel states, M2-brane 3-algebras, the Hanany-Witten rules, AdS3-gravity observables, supersymmetric indices of Coulomb branches as well as gauge/gravity duality between all these. We discuss this in the context of the hypothesis that the M-theory C-field is charge-quantized in Cohomotopy theory.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"151 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76845575","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: 20
Deformations of holomorphic pairs and $2d$-$4d$ wall-crossing 全纯对的变形和$2d$-$4d$壁交
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-12-20 DOI: 10.4310/ATMP.2022.v26.n6.a4
Veronica Fantini
{"title":"Deformations of holomorphic pairs and $2d$-$4d$ wall-crossing","authors":"Veronica Fantini","doi":"10.4310/ATMP.2022.v26.n6.a4","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n6.a4","url":null,"abstract":"We show how wall-crossing formulas in coupled 2d-4d systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a holomorphic vector bundle. The main part of the paper studies the relation between scattering diagrams and deformations of holomorphic pairs, building on recent work by Chan, Conan Leung and Ma.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"41 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76370252","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: 3
Computation of Kontsevich weights of connection and curvature graphs for symplectic Poisson structures 辛泊松结构连接图和曲率图的Kontsevich权的计算
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-12-18 DOI: 10.4310/atmp.2021.v25.n5.a5
Nima Moshayedi, F. Musio
{"title":"Computation of Kontsevich weights of connection and curvature graphs for symplectic Poisson structures","authors":"Nima Moshayedi, F. Musio","doi":"10.4310/atmp.2021.v25.n5.a5","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n5.a5","url":null,"abstract":"We give an explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture for symplectic manifolds. Moreover, we consider the case of a cotangent bundle, which will simplify the curvature expression significantly.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"172 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72917053","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
Module constructions for certain subgroups of the largest Mathieu group 最大Mathieu群的若干子群的模构造
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-12-09 DOI: 10.4310/atmp.2021.v25.n7.a2
Lea Beneish
{"title":"Module constructions for certain subgroups of the largest Mathieu group","authors":"Lea Beneish","doi":"10.4310/atmp.2021.v25.n7.a2","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n7.a2","url":null,"abstract":"For certain subgroups of $M_{24}$, we give vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms. These meromorphic Jacobi forms are canonically associated to the mock modular forms of Mathieu moonshine. The construction is related to the Conway moonshine module and employs a technique introduced by Anagiannis--Cheng--Harrison. With this construction we are able to give concrete vertex algebraic realizations of certain cuspidal Hecke eigenforms of weight two. In particular, we give explicit realizations of trace functions whose integralities are equivalent to divisibility conditions on the number of $mathbb{F}_p$ points on the Jacobians of modular curves.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"32 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72523860","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: 2
Adjoint Reidemeister torsions from wrapped M5-branes 缠绕m5膜的伴随赖德梅斯特扭转
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-11-25 DOI: 10.4310/ATMP.2021.v25.n7.a4
Dongmin Gang, Seonhwa Kim, Seokbeom Yoon
{"title":"Adjoint Reidemeister torsions from wrapped M5-branes","authors":"Dongmin Gang, Seonhwa Kim, Seokbeom Yoon","doi":"10.4310/ATMP.2021.v25.n7.a4","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n7.a4","url":null,"abstract":"We introduce a vanishing property of adjoint Reidemeister torsions of a cusped hyperbolic 3-manifold derived from the physics of wrapped M5-branes on the manifold. To support our physical observation, we present a rigorous proof for the figure-eight knot complement with respect to all slopes. We also present numerical verification for several knots.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"28 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78328423","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: 10
$frac{1}{2}$Calabi–Yau $4$-folds and four-dimensional F-theory on Calabi–Yau $4$-folds with $mathrm{U}(1)$ factors $frac{1}{2}$ Calabi-Yau $4$-fold与$ mathm {U}(1)$因子的Calabi-Yau $4$-fold的四维f理论
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-11-06 DOI: 10.4310/ATMP.2021.v25.n8.a3
Y. Kimura
{"title":"$frac{1}{2}$Calabi–Yau $4$-folds and four-dimensional F-theory on Calabi–Yau $4$-folds with $mathrm{U}(1)$ factors","authors":"Y. Kimura","doi":"10.4310/ATMP.2021.v25.n8.a3","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n8.a3","url":null,"abstract":"In this study, four-dimensional $N=1$ F-theory models with multiple U(1) gauge group factors are constructed. A class of rational elliptic 4-folds, which we call as \"$frac{1}{2}$Calabi-Yau 4-folds,\" is introduced, and we construct the elliptically fibered 4-folds by utilizing them. This yields a novel approach for building families of elliptically fibered Calabi-Yau 4-folds with positive Mordell-Weil ranks. The introduced $frac{1}{2}$Calabi-Yau 4-folds possess the characteristic property wherein the sum of the ranks of the singularity type and the Mordell-Weil group is always equal to six. This interesting property enables us to construct the elliptically fibered Calabi-Yau 4-folds of various positive Mordell-Weil ranks. From one to six U(1) factors form in four-dimensional F-theory on the resulting Calabi-Yau 4-folds. We also propose the geometric condition on the base 3-fold of the built Calabi-Yau 4-folds that allows four-dimensional F-theory models that have heterotic duals to be distinguished from those that do not.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"141 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80160515","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: 4
On gerbe duality and relative Gromov–Witten theory gerbe对偶性与相对Gromov-Witten理论
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-10-09 DOI: 10.4310/atmp.2021.v25.n8.a5
Xiang Tang, Hsian-Hua Tseng
{"title":"On gerbe duality and relative Gromov–Witten theory","authors":"Xiang Tang, Hsian-Hua Tseng","doi":"10.4310/atmp.2021.v25.n8.a5","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n8.a5","url":null,"abstract":". We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"40 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81624775","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: 1
Higher-spin kinematics & no ghosts on quantum space-time in Yang–Mills matrix models 杨-米尔斯矩阵模型中量子时空的高自旋运动学和无鬼
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-10-02 DOI: 10.4310/atmp.2021.v25.n4.a4
H. Steinacker
{"title":"Higher-spin kinematics & no ghosts on quantum space-time in Yang–Mills matrix models","authors":"H. Steinacker","doi":"10.4310/atmp.2021.v25.n4.a4","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n4.a4","url":null,"abstract":"A classification of bosonic on- and off-shell modes on a cosmological quantum space-time solution of the IIB matrix model is given, which leads to a higher-spin gauge theory. In particular, the no-ghost-theorem is established. The physical on-shell modes consist of 2 towers of higher-spin modes, which are effectively massless but include would-be massive degrees of freedom. The off-shell modes consist of 4 towers of higher-spin modes, one of which was missing previously. The noncommutativity leads to a cutoff in spin, which disappears in the semi-classical limit. An explicit basis allows to obtain the full propagator, which is governed by a universal effective metric. The physical metric fluctuations arise from would-be massive spin 2 modes, which were previously shown to include the linearized Schwarzschild solution. Due to the relation with ${cal N}=4$ super-Yang-Mills, this is expected to define a consistent quantum theory in 3+1 dimensions, which includes gravity.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"55 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79834304","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: 14
Unifying lattice models, links and quantum geometric Langlands via branes in string theory 弦理论中通过膜统一晶格模型、链接和量子几何朗兰
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2019-10-02 DOI: 10.4310/ATMP.2020.v24.n7.a1
M. Ashwinkumar, M. Tan
{"title":"Unifying lattice models, links and quantum geometric Langlands via branes in string theory","authors":"M. Ashwinkumar, M. Tan","doi":"10.4310/ATMP.2020.v24.n7.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2020.v24.n7.a1","url":null,"abstract":"We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Chern-Simons theory, (iii) the quantum geometric Langlands correspondence realized by Kapustin-Witten using 4d N = 4 gauge theory and its quantum group modification, and (iv) the Gaitsgory-Lurie conjecture relating quantum groups/affine Kac-Moody algebras to Whittaker D-modules/W-algebras. This furnishes, purely physically via branes in string theory, a novel bridge between the mathematics of integrable systems, geometric topology, geometric representation theory, and quantum algebras.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"8 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77106956","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: 6
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