Pub Date : 2019-05-22DOI: 10.4310/atmp.2020.v24.n7.a2
K. Costello, Si Li
We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for open-closed topological B-model. At one loop this anomaly cancellation is analogous to the Green-Schwarz mechanism. As an application, we introduce a type I version of Kodaira-Spencer theory in complex dimensions 3 and 5. In complex dimension 5, we show that it can only be coupled consistently at the quantum level to holomorphic Chern-Simons theory with gauge group SO(32). This is analogous to the Green-Schwarz mechanism for the physical type I string. This coupled system is conjectured to be a supersymmetric localization of type I string theory. In complex dimension 3, the required gauge group is SO(8).
{"title":"Anomaly cancellation in the topological string","authors":"K. Costello, Si Li","doi":"10.4310/atmp.2020.v24.n7.a2","DOIUrl":"https://doi.org/10.4310/atmp.2020.v24.n7.a2","url":null,"abstract":"We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for open-closed topological B-model. At one loop this anomaly cancellation is analogous to the Green-Schwarz mechanism. \u0000As an application, we introduce a type I version of Kodaira-Spencer theory in complex dimensions 3 and 5. In complex dimension 5, we show that it can only be coupled consistently at the quantum level to holomorphic Chern-Simons theory with gauge group SO(32). This is analogous to the Green-Schwarz mechanism for the physical type I string. This coupled system is conjectured to be a supersymmetric localization of type I string theory. In complex dimension 3, the required gauge group is SO(8).","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"9 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86044501","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 : 2019-05-22DOI: 10.4310/ATMP.2022.v26.n3.a2
G. Canepa, M. Schiavina
We compute the extension of the BV theory for three-dimensional General Relativity to all higher-codimension strata - boundaries, corners and vertices - in the BV-BFV framework. Moreover, we show that such extension is strongly equivalent to (nondegenerate) BF theory at all codimensions.
{"title":"Fully extended BV-BFV description of General Relativity in three dimensions","authors":"G. Canepa, M. Schiavina","doi":"10.4310/ATMP.2022.v26.n3.a2","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n3.a2","url":null,"abstract":"We compute the extension of the BV theory for three-dimensional General Relativity to all higher-codimension strata - boundaries, corners and vertices - in the BV-BFV framework. Moreover, we show that such extension is strongly equivalent to (nondegenerate) BF theory at all codimensions.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"42 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89792957","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 : 2019-05-20DOI: 10.4310/atmp.2020.v24.n5.a1
B. Dubrovin, Di Yang
Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.
研究标量非线性偏微分方程的拟平凡性的显式表达式。
{"title":"Remarks on intersection numbers and integrable hierarchies, I: Quasi-triviality","authors":"B. Dubrovin, Di Yang","doi":"10.4310/atmp.2020.v24.n5.a1","DOIUrl":"https://doi.org/10.4310/atmp.2020.v24.n5.a1","url":null,"abstract":"Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"10 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90754995","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 : 2019-03-28DOI: 10.4310/atmp.2022.v26.n5.a7
Usman Naseer, B. Zwiebach
We apply recently developed convex programs to find the minimal-area Riemannian metric on $2n$-sided polygons ($ngeq 3$) with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with the conformal extremal metric on the regular $2n$-gon. The hexagon was considered by Calabi. The region covered by the maximal number $n$ of geodesics bands extends over most of the surface and exhibits positive curvature. As $nto infty$ the metric, away from the boundary, approaches the well-known round extremal metric on $mathbb{RP}_2$. We extend Calabi's isosystolic variational principle to the case of regions with more than three bands of systolic geodesics. The extremal metric on $mathbb{RP}_2$ is a stationary point of this functional applied to a surface with infinite number of systolic bands.
{"title":"Extremal isosystolic metrics with multiple bands of crossing geodesics","authors":"Usman Naseer, B. Zwiebach","doi":"10.4310/atmp.2022.v26.n5.a7","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n5.a7","url":null,"abstract":"We apply recently developed convex programs to find the minimal-area Riemannian metric on $2n$-sided polygons ($ngeq 3$) with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with the conformal extremal metric on the regular $2n$-gon. The hexagon was considered by Calabi. The region covered by the maximal number $n$ of geodesics bands extends over most of the surface and exhibits positive curvature. As $nto infty$ the metric, away from the boundary, approaches the well-known round extremal metric on $mathbb{RP}_2$. We extend Calabi's isosystolic variational principle to the case of regions with more than three bands of systolic geodesics. The extremal metric on $mathbb{RP}_2$ is a stationary point of this functional applied to a surface with infinite number of systolic bands.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"161 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90541911","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 : 2019-03-21DOI: 10.4310/atmp.2022.v26.n5.a2
Daniel Grady, H. Sati
We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. In addition to providing a new conceptual framework and a mathematically solid setting, this allows us to uncover interesting and novel effects. Explicitly, we use our recently constructed Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential K-theory to characterize the RR fields and their quantization, which involves interesting interplay between geometric and topological data. We illustrate this with the examples of spheres, tori, and Calabi-Yau threefolds.
{"title":"Ramond–Ramond fields and twisted differential K-theory","authors":"Daniel Grady, H. Sati","doi":"10.4310/atmp.2022.v26.n5.a2","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n5.a2","url":null,"abstract":"We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. In addition to providing a new conceptual framework and a mathematically solid setting, this allows us to uncover interesting and novel effects. Explicitly, we use our recently constructed Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential K-theory to characterize the RR fields and their quantization, which involves interesting interplay between geometric and topological data. We illustrate this with the examples of spheres, tori, and Calabi-Yau threefolds.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"14 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82647947","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 : 2019-03-21DOI: 10.4310/atmp.2019.v23.n8.a1
Aghil Alaee, Armando J. Cabrera Pacheco, Carla Cederbaum
The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the ADM mass of these extensions is well-controlled, and thus, they were able to compute the Bartnik mass for minimal spheres satisfying a stability condition. In this work, we develop extensions and gluing tools, a la Mantoulidis and Schoen, for time-symmetric initial data sets for the Einstein-Maxwell equations that allow us to compute the value of an ad-hoc notion of charged Barnik mass for suitable charged minimal Bartnik data.
{"title":"Asymptotically flat extensions with charge","authors":"Aghil Alaee, Armando J. Cabrera Pacheco, Carla Cederbaum","doi":"10.4310/atmp.2019.v23.n8.a1","DOIUrl":"https://doi.org/10.4310/atmp.2019.v23.n8.a1","url":null,"abstract":"The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the ADM mass of these extensions is well-controlled, and thus, they were able to compute the Bartnik mass for minimal spheres satisfying a stability condition. In this work, we develop extensions and gluing tools, a la Mantoulidis and Schoen, for time-symmetric initial data sets for the Einstein-Maxwell equations that allow us to compute the value of an ad-hoc notion of charged Barnik mass for suitable charged minimal Bartnik data.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"23 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75832121","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 : 2019-03-10DOI: 10.4310/atmp.2022.v26.n5.a1
Kowshik Bettadapura
On a group $G$, a filtration by normal subgroups is referred to as a normal series. If subsequent quotients are abelian, the filtration is referred to as an emph{abelian-quotient normal series}, or `AQ normal series' for short. In this article we consider `sheaves of AQ normal series'. From a given AQ normal series satisfying an additional hypothesis we derive a complex whose first cohomology obstructs the resolution of an `integration problem'. These constructs are then applied to the classification of supermanifolds modelled on $(X, T^*_{X, -})$, where $X$ is a complex manifold and $T^*_{X, -}$ is a holomorphic vector bundle. We are lead to the notion of an `obstruction complex' associated to a model $(X, T^*_{X, -})$ whose cohomology is referred to as `obstruction cohomology'. We deduce a number of interesting consequences of a vanishing first obstruction cohomology. Among the more interesting consequences are its relation to projectability of supermanifolds and a `Batchelor-type' theorem: if the obstruction cohomology of a `good' model $(X, T^*_{X, -})$ vanishes, then any supermanifold modelled on $(X, T^*_{X, -})$ will be split.
{"title":"Sheaves of AQ normal series and supermanifolds","authors":"Kowshik Bettadapura","doi":"10.4310/atmp.2022.v26.n5.a1","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n5.a1","url":null,"abstract":"On a group $G$, a filtration by normal subgroups is referred to as a normal series. If subsequent quotients are abelian, the filtration is referred to as an emph{abelian-quotient normal series}, or `AQ normal series' for short. In this article we consider `sheaves of AQ normal series'. From a given AQ normal series satisfying an additional hypothesis we derive a complex whose first cohomology obstructs the resolution of an `integration problem'. These constructs are then applied to the classification of supermanifolds modelled on $(X, T^*_{X, -})$, where $X$ is a complex manifold and $T^*_{X, -}$ is a holomorphic vector bundle. We are lead to the notion of an `obstruction complex' associated to a model $(X, T^*_{X, -})$ whose cohomology is referred to as `obstruction cohomology'. We deduce a number of interesting consequences of a vanishing first obstruction cohomology. Among the more interesting consequences are its relation to projectability of supermanifolds and a `Batchelor-type' theorem: if the obstruction cohomology of a `good' model $(X, T^*_{X, -})$ vanishes, then any supermanifold modelled on $(X, T^*_{X, -})$ will be split.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"48 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77231728","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 : 2019-03-02DOI: 10.4310/atmp.2021.v25.n4.a1
H. Braden, V. Enolski
Recently we have shown how one may use use integrable systems techniques to implement the ADHMN construction and obtain general analytic formulae for the charge n su(2) Euclidean monopole. Here we do this for the case of charge 2: so answering an open problem of some 30 years standing. A comparison with known results and other approaches is made and new results presented.
{"title":"The charge $2$ monopole via the ADHMN construction","authors":"H. Braden, V. Enolski","doi":"10.4310/atmp.2021.v25.n4.a1","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n4.a1","url":null,"abstract":"Recently we have shown how one may use use integrable systems techniques to implement the ADHMN construction and obtain general analytic formulae for the charge n su(2) Euclidean monopole. Here we do this for the case of charge 2: so answering an open problem of some 30 years standing. A comparison with known results and other approaches is made and new results presented.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"2005 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82978604","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 : 2019-02-19DOI: 10.4310/ATMP.2022.v26.n4.a2
Kengo Kikuchi
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components of conformal groups acting on various metric spaces using a simple fact; given local coordinate systems be single-valued. Boundary conditions thus obtained which must be satisfied by conformal Killing vectors (CKVs) correctly reproduce known conformal groups. As a byproduct, on $mathbb S^1_ltimesmathbb H^2_r$, by setting their radii $l=Nr$ with $Ninmathbb N^times$, we find (the identity component of) the conformal group enhances, whose persistence in higher dimensions is also argued. We also discuss forms of correlation functions on these spaces using the symmetries. Finally, we study a $d$-torus $mathbb T^d$ in detail, and show the identity component of the conformal group acting on the manifold in general is given by $text{Conf}_0(mathbb T^d)simeq U(1)^d$ when $dge2$. Using the fact, we suggest some candidates of conformal manifolds of CFTs on $mathbb T^d$ without assuming the presence of supersymmetry (SUSY). In order to clarify which parts of correlation functions are physical, we also discuss renormalization group (RG) and local counterterms on curved spaces.
{"title":"CFTs on curved spaces","authors":"Kengo Kikuchi","doi":"10.4310/ATMP.2022.v26.n4.a2","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n4.a2","url":null,"abstract":"We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components of conformal groups acting on various metric spaces using a simple fact; given local coordinate systems be single-valued. Boundary conditions thus obtained which must be satisfied by conformal Killing vectors (CKVs) correctly reproduce known conformal groups. As a byproduct, on $mathbb S^1_ltimesmathbb H^2_r$, by setting their radii $l=Nr$ with $Ninmathbb N^times$, we find (the identity component of) the conformal group enhances, whose persistence in higher dimensions is also argued. We also discuss forms of correlation functions on these spaces using the symmetries. Finally, we study a $d$-torus $mathbb T^d$ in detail, and show the identity component of the conformal group acting on the manifold in general is given by $text{Conf}_0(mathbb T^d)simeq U(1)^d$ when $dge2$. Using the fact, we suggest some candidates of conformal manifolds of CFTs on $mathbb T^d$ without assuming the presence of supersymmetry (SUSY). In order to clarify which parts of correlation functions are physical, we also discuss renormalization group (RG) and local counterterms on curved spaces.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90053851","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 : 2019-02-03DOI: 10.4310/ATMP.2021.v25.n5.a4
Y. Kimura
Eight-dimensional non-geometric heterotic strings with gauge algebra $mathfrak{e}_8mathfrak{e}_7$ were constructed by Malmendier and Morrison as heterotic duals of F-theory on K3 surfaces with $Lambda^{1,1}oplus E_8oplus E_7$ lattice polarization. Clingher, Malmendier and Shaska extended these constructions to eight-dimensional non-geometric heterotic strings with gauge algebra $mathfrak{e}_7mathfrak{e}_7$ as heterotic duals of F-theory on $Lambda^{1,1}oplus E_7oplus E_7$ lattice polarized K3 surfaces. In this study, we analyze the points in the moduli of non-geometric heterotic strings with gauge algebra $mathfrak{e}_7mathfrak{e}_7$, at which the non-Abelian gauge groups on the F-theory side are maximally enhanced. The gauge groups on the heterotic side do not allow for the perturbative interpretation at these points. We show that these theories can be described as deformations of the stable degenerations, as a result of coincident 7-branes on the F-theory side. From the heterotic viewpoint, this effect corresponds to the insertion of 5-branes. These effects can be used to understand nonperturbative aspects of nongeometric heterotic strings. Additionally, we build a family of elliptic Calabi-Yau 3-folds by fibering elliptic K3 surfaces, which belong to the F-theory side of the moduli of non-geometric heterotic strings with gauge algebra $mathfrak{e}_7mathfrak{e}_7$, over $mathbb{P}^1$. We find that highly enhanced gauge symmetries arise on F-theory on the built elliptic Calabi-Yau 3-folds.
{"title":"Unbroken $E7 times E7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals","authors":"Y. Kimura","doi":"10.4310/ATMP.2021.v25.n5.a4","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n5.a4","url":null,"abstract":"Eight-dimensional non-geometric heterotic strings with gauge algebra $mathfrak{e}_8mathfrak{e}_7$ were constructed by Malmendier and Morrison as heterotic duals of F-theory on K3 surfaces with $Lambda^{1,1}oplus E_8oplus E_7$ lattice polarization. Clingher, Malmendier and Shaska extended these constructions to eight-dimensional non-geometric heterotic strings with gauge algebra $mathfrak{e}_7mathfrak{e}_7$ as heterotic duals of F-theory on $Lambda^{1,1}oplus E_7oplus E_7$ lattice polarized K3 surfaces. In this study, we analyze the points in the moduli of non-geometric heterotic strings with gauge algebra $mathfrak{e}_7mathfrak{e}_7$, at which the non-Abelian gauge groups on the F-theory side are maximally enhanced. The gauge groups on the heterotic side do not allow for the perturbative interpretation at these points. We show that these theories can be described as deformations of the stable degenerations, as a result of coincident 7-branes on the F-theory side. From the heterotic viewpoint, this effect corresponds to the insertion of 5-branes. These effects can be used to understand nonperturbative aspects of nongeometric heterotic strings. Additionally, we build a family of elliptic Calabi-Yau 3-folds by fibering elliptic K3 surfaces, which belong to the F-theory side of the moduli of non-geometric heterotic strings with gauge algebra $mathfrak{e}_7mathfrak{e}_7$, over $mathbb{P}^1$. We find that highly enhanced gauge symmetries arise on F-theory on the built elliptic Calabi-Yau 3-folds.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"116 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77166627","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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