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4d/2d → 3d/1d: A song of protected operator algebras 4d/2d→3d/1d:保护算子代数之歌
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.4310/atmp.2022.v26.n7.a2
M. Dedushenko, Yifan Wang
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引用次数: 15
Bifurcations and chaos in Hořava–Lifshitz cosmology Hořava-Lifshitz宇宙学中的分岔和混沌
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.4310/atmp.2022.v26.n7.a4
J. Hell, Phillipo Lappicy, C. Uggla
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引用次数: 1
Positive energy representations of affine algebras and Stokes matrices of the affine Toda equations 仿射代数的正能量表示和仿射Toda方程的Stokes矩阵
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-09-02 DOI: 10.4310/atmp.2022.v26.n7.a3
M. Guest, T. Otofuji
We give a construction which produces a positive energy representation of the affine Lie algebra of type A_n from the Stokes data of a solution of the tt*-Toda equations of type A_n. The construction appears to play a role in conformal field theory. We illustrate this with several examples: the fusion ring, W-algebra minimal models (Argyres-Douglas theory), as well as topological-antitopological fusion itself. (Minor typographical changes for this version.)
利用A_n型的tt*-Toda方程的一个解的Stokes数据,给出了一个构造,可以得到A_n型仿射李代数的正能量表示。这种结构似乎在共形场论中发挥了作用。我们用几个例子来说明这一点:融合环,w代数最小模型(Argyres-Douglas理论),以及拓扑-反拓扑融合本身。(本版本的排版略有变化。)
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引用次数: 2
Probing the Big Bang with quantum fields 用量子场探测宇宙大爆炸
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-07-18 DOI: 10.4310/ATMP.2021.v25.n7.a1
A. Ashtekar, T. Lorenzo, M. Schneider
By carrying out a systematic investigation of linear, test quantum fields φ̂(x) in cosmological space-times, we show that φ̂(x) remain well-defined across the big bang as operator valued distributions in a large class of Friedmann, Lemâıtre, Robertson, Walker space-times, including radiation and dust filled universes. In particular, the expectation values 〈φ̂(x) φ̂(x ′)〉 are well-defined bi-distributions in the extended space-time in spite of the big bang singularity. Interestingly, correlations between fields evaluated at spatially and temporally separated points exhibit an asymmetry that is reminiscent of the Belinskii, Khalatnikov, Lifshitz behavior. The renormalized products of fields 〈φ̂(x)〉ren and 〈T̂ab(x)〉ren also remain well-defined as distributions. Conformal coupling is not necessary for these considerations to hold. Thus, when probed with observables associated with quantum fields, the big bang (and the big crunch) singularities are quite harmless.
通过对宇宙学时空中线性、测试量子场φ φ (x)的系统研究,我们表明φ φ (x)在大爆炸中作为算子值分布在一大类弗里德曼、Lemâıtre、罗伯逊、沃克时空中(包括辐射和充满尘埃的宇宙)仍然是定义良好的。特别是,尽管存在大爆炸奇点,期望值< φ φ (x) φ φ (x’)>在扩展时空中是定义良好的双分布。有趣的是,在空间和时间分离的点上评估的场之间的相关性表现出一种不对称,这让人想起Belinskii, Khalatnikov, Lifshitz行为。场< φ³(x) > ren和< T³ab(x) > ren的重整化积也仍然是定义良好的分布。对于这些考虑,保角耦合不是必须的。因此,当用与量子场相关的可观测物进行探测时,大爆炸(和大压缩)奇点是相当无害的。
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引用次数: 8
Shifted symplectic reduction of derived critical loci 导出临界轨迹的移位辛约简
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-06-11 DOI: 10.4310/ATMP.2022.v26.n6.a1
M. Anel, D. Calaque
We prove that the derived critical locus of a $G$-invariant function $S:Xtomathbb{A}^1$ carries a shifted moment map, and that its derived symplectic reduction is the derived critical locus of the induced function $S_{red}:X/Gtomathbb{A}^1$ on the orbit stack. We also provide a relative version of this result, and show that derived symplectic reduction commutes with derived lagrangian intersections.
我们证明了$G$不变函数$S:Xtomathbb{a}^1$的导出临界轨迹携带一个位移矩映射,并且它的导出辛约化是诱导函数$S_{red}:X/Gtomathbb{a}^1$在轨道堆栈上的导出临界轨迹。我们还提供了这个结果的一个相对版本,并证明了导出的辛约简与导出的拉格朗日交点交换。
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引用次数: 5
General couplings of four dimensional Maxwell–Klein–Gordon system: Global existence 四维Maxwell-Klein-Gordon系统的一般耦合:全局存在性
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-05-25 DOI: 10.4310/atmp.2022.v26.n1.a4
Mulyanto, F. Akbar, B. Gunara
In this paper, we consider the multi component fields interactions of the complex scalar fields and the electromagnetic fields (Maxwell-Klein-Gordon system) on four dimensional Minkowski spacetime with general gauge couplings and the scalar potential turned on. Moreover, the complex scalar fields span an internal manifold assumed to be Kähler. Then, by taking the Kähler potential to be bounded by U(1)N symmetric Kähler potential, the gauge couplings to be bounded functions, and the scalar potential to be the form of either polynomial, sine-Gordon, or Toda potential, we prove the global existence of the system.
本文考虑了四维闵可夫斯基时空中具有一般规范耦合和开启标量势的复标量场与电磁场(麦克斯韦-克莱因-戈登系统)的多分量场相互作用。此外,复标量场张成一个假定为Kähler的内部流形。然后,通过取以U(1)N个对称Kähler势为界的Kähler势,规范耦合为有界函数,标量势为多项式、sin - gordon或Toda势的形式,证明了系统的整体存在性。
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引用次数: 1
Algebraic interplay between renormalization and monodromy 重整化与单态之间的代数相互作用
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-05-12 DOI: 10.4310/ATMP.2023.v27.n1.a4
D. Kreimer, K. Yeats
We investigate combinatorial and algebraic aspects of the interplay between renormalization and monodromies for Feynman amplitudes. We clarify how extraction of subgraphs from a Feynman graph interacts with putting edges onshell or with contracting them to obtain reduced graphs. Graph by graph this leads to a study of cointeracting bialgebras. One bialgebra comes from extraction of subgraphs and hence is needed for renormalization. The other bialgebra is an incidence bialgebra for edges put either on- or offshell. It is hence related to the monodromies of the multivalued function to which a renormalized graph evaluates. Summing over infinite series of graphs, consequences for Green functions are derived using combinatorial Dyson--Schwinger equations.
我们研究了费曼振幅的重整化和单态之间相互作用的组合和代数方面。我们阐明了如何从费曼图中提取子图与将边放在壳上或收缩它们以获得约简图的相互作用。一个图接一个图,这导致了对互作用双代数的研究。一个双代数来自子图的提取,因此需要进行重整化。另一个双代数是置于壳上或壳外的边的关联双代数。因此,它与重归一化图求值的多值函数的单态有关。对无穷级数的图求和,使用组合Dyson- Schwinger方程推导出Green函数的结果。
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引用次数: 11
Supertranslation invariance of angular momentum 角动量的超平移不变性
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-02-05 DOI: 10.4310/atmp.2021.v25.n3.a4
Po-Ning Chen, Mu-Tao Wang, Ye-Kai Wang, S. Yau
LIGO’s successful detection of gravitational waves has revitalized the theoretical understanding of the angular momentum carried away by gravitational radiation. An infinite dimensional supertranslation ambiguity has presented an essential difficulty for decades of study. Recent advances were made to address and quantify the supertranslation ambiguity in the context of compact binary coalescence. Here we present the first definition of angular momentum in general relativity that is completely free from supertranslation ambiguity. The new definition was derived from the limit of the quasilocal angular momentum defined previously by the authors. A new definition of center of mass at null infinity is also proposed and shown to be supertranslation invariant. Together with the classical Bondi-Sachs energy-momentum, they form a complete set of conserved quantities at null infinity that transform according to basic physical laws.
LIGO对引力波的成功探测,重新激活了对引力波辐射带来的角动量的理论理解。无限维的超翻译歧义是几十年来研究的一个重要难题。最近的进展作出了解决和量化超翻译歧义在紧凑的二进制合并的背景下。在这里,我们提出了广义相对论中角动量的第一个定义,它完全没有超平移歧义。新的定义是由作者先前定义的准局部角动量的极限推导出来的。提出了零无穷远处质心的一个新定义,并证明了它是超平移不变量。与经典的Bondi-Sachs能量动量一起,它们在零无穷处形成了一套完整的守恒量,根据基本物理定律进行变换。
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引用次数: 23
Almost contact structures on manifolds with a $G_2$ structure 具有G_2结构的流形上的几乎接触结构
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-01-29 DOI: 10.4310/atmp.2022.v26.n1.a3
Xenia de la Ossa, M. Larfors, Matthew Magill
We review the construction of almost contact metric (three-) structures on manifolds with a G2 structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the SU(3) structure associated to an ACMS and apply these computations to heterotic G2 systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed. ar X iv :2 10 1. 12 60 5v 1 [ he pth ] 2 9 Ja n 20 21
本文讨论了具有G2结构的流形上几乎接触度量(三)结构的构造。这些对于弦和m理论中的某些超对称构型是有意义的。我们计算了与ACMS相关的SU(3)结构的扭转,并将这些计算应用于异质G2系统和超对称增强。我们发起了acm3s空间的研究,它是一个具有局部积结构和有趣拓扑特征的无限维空间。观察到acm3s与结合子流形和协结合子流形之间的诱人联系。ar X iv:2 10 1。[au:] [au:] [au:] [au:
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引用次数: 5
The duality covariant geometry and DSZ quantization of abelian gauge theory 阿贝尔规范理论的对偶协变几何与DSZ量化
IF 1.5 4区 物理与天体物理 Q1 Mathematics Pub Date : 2021-01-18 DOI: 10.4310/atmp.2022.v26.n7.a5
C. Lazaroiu, C. Shahbazi
We develop the Dirac-Schwinger-Zwanziger (DSZ) quantization of classical abelian gauge theories with general duality structure on oriented Lorentzian four-manifolds $(M,g)$ of arbitrary topology, obtaining, as a result, the duality-covariant geometric formulation of such theories through connections on principal bundles. We implement the DSZ condition by restricting the field strengths of the theory to those which define classes originating in the degree-two cohomology of a local system valued in the groupoid of integral symplectic spaces. We prove that such field strengths are curvatures of connections $mathcal{A}$ defined on principal bundles $P$ whose structure group $G$ is the disconnected group of automorphisms of an integral affine symplectic torus. The connected component of the identity of $G$ is a torus group, while its group of connected components is a modified Siegel modular group. This formulation includes electromagnetic and magnetoelectric gauge potentials on an equal footing and describes the equations of motion through a first-order polarized self-duality condition for the curvature of $mathcal{A}$. The condition involves a combination of the Hodge operator of $(M,g)$ with a taming of the duality structure determined by $P$, whose choice encodes the self-couplings of the theory. This description is reminiscent of the theory of four-dimensional euclidean instantons, even though we consider a two-derivative theory in Lorentzian signature. We use this formulation to characterize the hierarchy of duality groups of abelian gauge theory, providing a gauge-theoretic description of the electromagnetic duality group as the discrete remnant of the gauge group of $P$. We also perform the time-like reduction of the polarized self-duality condition to a Riemannian three-manifold, obtaining a new type of Bogomolny equation which we solve explicitly in a particular case.
在任意拓扑的有向洛伦兹四流形$(M,g)$上发展了具有一般对偶结构的经典阿贝规范理论的Dirac-Schwinger-Zwanziger (DSZ)量子化,从而通过主束上的连接得到了这类理论的对偶协变几何表达式。我们通过将理论的场强限定为那些定义了在积分辛空间的群上取值的局部系统的二次上同调中起源的类的场强来实现DSZ条件。我们证明了这样的场强是定义在主束P上的连接$mathcal{A}$的曲率,其结构群$G$是整仿射辛环面的自同构的不连通群。$G$的单位元的连通分量是一个环面群,而它的连通分量群是一个修正的Siegel模群。该公式包含了相等基础上的电磁和磁电规范电位,并通过曲率$mathcal{a}$的一阶极化自对偶条件描述了运动方程。该条件涉及$(M,g)$的Hodge算子与由$P$确定的对偶结构的驯服的组合,其选择编码了理论的自耦合。这种描述让人想起四维欧几里得瞬子理论,尽管我们考虑的是洛伦兹特征中的二阶导数理论。我们用这个公式刻画了阿贝尔规范论中对偶群的层次,给出了电磁对偶群作为P规范群的离散残馀的规范理论描述。我们还对极化自对偶条件进行了类时化简,得到了一类新的Bogomolny方程,并在特定情况下得到了显式解。
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Advances in Theoretical and Mathematical Physics
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