Pub Date : 2019-12-24DOI: 10.4310/ATMP.2021.v25.n7.a5
Santosh Kandel, P. Mnev, K. Wernli
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.
{"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}
Pub Date : 2019-12-22DOI: 10.4310/atmp.2022.v26.n4.a4
H. Sati, U. Schreiber
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.
{"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}
Pub Date : 2019-12-20DOI: 10.4310/ATMP.2022.v26.n6.a4
Veronica Fantini
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.
{"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}
Pub Date : 2019-12-18DOI: 10.4310/atmp.2021.v25.n5.a5
Nima Moshayedi, F. Musio
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.
{"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}
Pub Date : 2019-12-09DOI: 10.4310/atmp.2021.v25.n7.a2
Lea Beneish
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.
{"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}
Pub Date : 2019-11-25DOI: 10.4310/ATMP.2021.v25.n7.a4
Dongmin Gang, Seonhwa Kim, Seokbeom Yoon
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.
{"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}
Pub Date : 2019-11-06DOI: 10.4310/ATMP.2021.v25.n8.a3
Y. Kimura
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.
{"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}
Pub Date : 2019-10-09DOI: 10.4310/atmp.2021.v25.n8.a5
Xiang Tang, Hsian-Hua Tseng
. We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.
． 我们提出并研究了gerbe对偶对相对Gromov-Witten理论的推广。
{"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}
Pub Date : 2019-10-02DOI: 10.4310/atmp.2021.v25.n4.a4
H. Steinacker
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.
{"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}
Pub Date : 2019-10-02DOI: 10.4310/ATMP.2020.v24.n7.a1
M. Ashwinkumar, M. Tan
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.
我们解释了如何从IIA型弦理论中以ns5膜为尾的d4膜的一堆开始，通过t对偶性和相关世界体积理论的拓扑全纯性，联系(i) Costello的4d chen - simons理论实现的晶格模型，(ii)三维解析连续chen - simons理论中的链接，(iii) Kapustin-Witten利用4d N = 4规范理论及其量子群修正实现的量子几何朗兰兹对应。(iv)量子群/仿射Kac-Moody代数与Whittaker d -模/ w -代数之间的Gaitsgory-Lurie猜想。这在纯物理上通过弦理论中的膜，在可积系统的数学、几何拓扑、几何表示理论和量子代数之间架起了一座新的桥梁。
{"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}
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