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Interface currents and corner states in magnetic quarter-plane systems 磁性四分之一平面系统中的界面电流和角态
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.a4
Danilo Polo Ojito
{"title":"Interface currents and corner states in magnetic quarter-plane systems","authors":"Danilo Polo Ojito","doi":"10.4310/atmp.2023.v27.n6.a4","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n6.a4","url":null,"abstract":"We study the propagation of currents along the interface of two $2$-$d$ magnetic systems, where one of them occupies the first quadrant of the plane. By considering the tight-binding approximation model and K-theory, we prove that, for an integer number that is given by the difference of two bulk topological invariants of each system, such interface currents are quantized. We further state the necessary conditions to produce corner states for these kinds of underlying systems, and we show that they have topologically protected asymptotic invariants.","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":"141721381","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
Conformal geometry and half-integrable spacetimes 共形几何与半积分时空
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.a1
Bernardo Araneda
{"title":"Conformal geometry and half-integrable spacetimes","authors":"Bernardo Araneda","doi":"10.4310/atmp.2023.v27.n6.a1","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n6.a1","url":null,"abstract":"Using a combination of techniques from conformal and complex geometry, we show the potentialization of 4‑dimensional closed Einstein–Weyl structures which are half-algebraically special and admit a “half-integrable” almost-complex structure. That is, we reduce the Einstein–Weyl equations to a single, conformally invariant, non-linear scalar equation, that we call the “conformal HH equation”, and we reconstruct the conformal structure (curvature and metric) from a solution to this equation. We show that the conformal metric is composed of: a conformally flat part, a conformally half-flat part related to certain “constants” of integration, and a potential part that encodes the full non-linear curvature, and that coincides in form with the Hertz potential from perturbation theory. We also study the potentialization of the Dirac–Weyl, Maxwell (with and without sources), and Yang–Mills systems. We show how to deal with the ordinary Einstein equations by using a simple trick. Our results give a conformally invariant, coordinatefree, generalization of the hyper-heavenly construction of Plebański and collaborators.","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":"141722439","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
MSW-type compactifications of 6d $(1,0)$ SCFTs on 4-manifolds 4-manifolds 上 6d $(1,0)$ SCFT 的 MSW 型压实
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.a5
Jin Chen, Zhuo Chen, Wei Cui, Babak Haghighat
{"title":"MSW-type compactifications of 6d $(1,0)$ SCFTs on 4-manifolds","authors":"Jin Chen, Zhuo Chen, Wei Cui, Babak Haghighat","doi":"10.4310/atmp.2023.v27.n6.a5","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n6.a5","url":null,"abstract":"$defd{mathrm{d}}$ In this work, we study compactifications of $6d$ $(1, 0)$ SCFTs, in particular those of conformal matter type, on Kähler 4-manifolds. We show how this can be realized via wrapping M5 branes on $4$-cycles of non-compact Calabi–Yau fourfolds with ADE singularity in the fiber. Such compactifications lead to domain walls in $3d$ $mathcal{N} = 2$ theories which flow to $2d N = (0, 2)$ SCFTs. We compute the central charges of such $2d$ CFTs via $6d$ anomaly polynomials by employing a particular topological twist along the $4$-manifold. Moreover, we study compactifications on non-compact $4$-manifolds leading to coupled $3d$-$2d$ systems. We show how these can be glued together consistently to reproduce the central charge and anomaly polynomial obtained in the compact case. Lastly, we study concrete CFT proposals for some special cases.","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":"141721380","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
Machine-learned Calabi–Yau metrics and curvature 机器学习 Calabi-Yau 度量和曲率
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI: 10.4310/atmp.2023.v27.n4.a3
Per Berglund, Giorgi Butbaia, Tristan Hüubsch, Vishnu Jejjala, Damián Mayorga Peña, Challenger Mishra, Justin Tan
{"title":"Machine-learned Calabi–Yau metrics and curvature","authors":"Per Berglund, Giorgi Butbaia, Tristan Hüubsch, Vishnu Jejjala, Damián Mayorga Peña, Challenger Mishra, Justin Tan","doi":"10.4310/atmp.2023.v27.n4.a3","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n4.a3","url":null,"abstract":"$defSingX{mathrm{Sing}X}$Finding Ricci-flat (Calabi–Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi–Yau metric within a given Kähler class. In this paper we investigate numerical Ricci-flat metrics over smooth and singular K3 surfaces and Calabi–Yau threefolds. Using these Ricci-flat metric approximations for the Cefalú family of quartic twofolds and the Dwork family of quintic threefolds, we study characteristic forms on these geometries. We observe that the numerical stability of the numerically computed topological characteristic is heavily influenced by the choice of the neural network model, in particular, we briefly discuss a different neural network model, namely spectral networks, which correctly approximate the topological characteristic of a Calabi–Yau. Using persistent homology, we show that high curvature regions of the manifolds form clusters near the singular points. For our neural network approximations, we observe a Bogomolov–Yau type inequality $3c_2 geq c^2_1$ and observe an identity when our geometries have isolated $A_1$ type singularities. We sketch a proof that $chi (X setminus SingX) + 2 {lvert SingX rvert} = 24$ also holds for our numerical approximations.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550607","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
Cluster transformations, the tetrahedron equation, and three-dimensional gauge theories 簇变换、四面体方程和三维规规理论
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI: 10.4310/atmp.2023.v27.n4.a2
Xiaoyue Sun, Junya Yagi
{"title":"Cluster transformations, the tetrahedron equation, and three-dimensional gauge theories","authors":"Xiaoyue Sun, Junya Yagi","doi":"10.4310/atmp.2023.v27.n4.a2","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n4.a2","url":null,"abstract":"We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three trivial cluster transformations with 8, 32 and 32 mutations. For each of these cluster transformations, a unitary operator representing a single braid move in a quantum mechanical system solves the tetrahedron equation. The solutions thus obtained are constructed from the noncompact quantum dilogarithm and can be identified with the partition functions of three-dimensional $mathcal{N} = 2$ supersymmetric gauge theories on a squashed three-sphere.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552940","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
Topology change with Morse functions: progress on the Borde–Sorkin conjecture 莫尔斯函数的拓扑变化：博尔德-索金猜想的进展
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI: 10.4310/atmp.2023.v27.n4.a4
Leonardo García-Heveling
{"title":"Topology change with Morse functions: progress on the Borde–Sorkin conjecture","authors":"Leonardo García-Heveling","doi":"10.4310/atmp.2023.v27.n4.a4","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n4.a4","url":null,"abstract":"Topology change is considered to be a necessary feature of quantum gravity by some authors, and impossible by others. One of the main arguments against it is that spacetimes with changing spatial topology have bad causal properties. Borde and Sorkin proposed a way to avoid this dilemma by considering topology changing spacetimes constructed from Morse functions, where the metric is allowed to vanish at isolated points. They conjectured that these Morse spacetimes are causally continuous (hence quite well behaved), as long as the index of the Morse points is different from $1$ and $n-1$. In this paper, we prove a special case of this conjecture. We also argue, heuristically, that the original conjecture is actually false, and formulate a refined version of it.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550608","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
A Green’s function for the source-free Maxwell Equations on $AdS^5 times S^2 times S^3$ A Green's function for the source-free Maxwell Equations on $AdS^5 times S^2 times S^3$
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI: 10.4310/atmp.2023.v27.n4.a5
Damien Gobin, Niky Kamran
{"title":"A Green’s function for the source-free Maxwell Equations on $AdS^5 times S^2 times S^3$","authors":"Damien Gobin, Niky Kamran","doi":"10.4310/atmp.2023.v27.n4.a5","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n4.a5","url":null,"abstract":"$defD{mathcal{D}}$We compute a Green’s function giving rise to the solution of the Cauchy problem for the source-free Maxwell’s equations on a causal domain $D$ contained in a geodesically normal domain of the Lorentzian manifold $AdS^5 times mathbb{S}^2 times mathbb{S}^3$, where $AdS^5$ denotes the simply connected $5$-dimensional anti-de-Sitter space-time. Our approach is to formulate the original Cauchy problem as an equivalent Cauchy problem for the Hodge Laplacian on $D$ and to seek a solution in the form of a Fourier expansion in terms of the eigenforms of the Hodge Laplacian on $mathbb{S}^3$. This gives rise to a sequence of inhomogeneous Cauchy problems governing the form-valued Fourier coefficients corresponding to the Fourier modes and involving operators related to the Hodge Laplacian on $AdS^5 times mathbb{S}^2$, which we solve explicitly by using Riesz distributions and the method of spherical means for differential forms. Finally we put together into the Fourier expansion on $mathbb{S}^3$ the modes obtained by this procedure, producing a $2$-form on $D subset AdS^5 times mathbb{S}^2 times mathbb{S}^3$ which we show to be a solution of the original Cauchy problem for Maxwell’s equations.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552956","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
On the construction of fuzzy spaces and modules over shift algebras 论模糊空间和移位代数模块的构建
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI: 10.4310/atmp.2023.v27.n4.a6
Joakim Arnlind, Andreas Sykora
{"title":"On the construction of fuzzy spaces and modules over shift algebras","authors":"Joakim Arnlind, Andreas Sykora","doi":"10.4310/atmp.2023.v27.n4.a6","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n4.a6","url":null,"abstract":"We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out that the structure of these modules depends in a crucial way on the properties of the function spaces. Moreover, for a class of subalgebras related to compact manifolds, we provide a construction procedure for the corresponding fuzzy spaces, i.e. sequences of finite dimensional modules of increasing dimension as the deformation parameter tends to zero, as well as infinite dimensional modules related to fuzzy non-compact spaces.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552779","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
From equivariant volumes to equivariant periods 从等变体积到等变周期
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI: 10.4310/atmp.2023.v27.n4.a1
Luca Cassia, Nicolò Piazzalunga, Maxim Zabzine
{"title":"From equivariant volumes to equivariant periods","authors":"Luca Cassia, Nicolò Piazzalunga, Maxim Zabzine","doi":"10.4310/atmp.2023.v27.n4.a1","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n4.a1","url":null,"abstract":"We consider generalizations of equivariant volumes of abelian GIT quotients obtained as partition functions of 1d, 2d, and 3d supersymmetric GLSM on $S^1$, $D^2$ and $D^2 times S^1$, respectively. We define these objects and study their dependence on equivariant parameters for non-compact toric Kähler quotients. We generalize the finite-difference equations (shift equations) obeyed by equivariant volumes to these partition functions. The partition functions are annihilated by differential/difference operators that represent equivariant quantum cohomology/K-theory relations of the target and the appearance of compact divisors in these relations plays a crucial role in the analysis of the non-equivariant limit. We show that the expansion in equivariant parameters contains information about genus-zero Gromov–Witten invariants of the target.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550606","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
On the complex affine structures of SYZ-fibration of del Pezzo surfaces del Pezzo表面syz -纤化的复杂仿射结构
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2023-06-30 DOI: 10.4310/atmp.2022.v26.n6.a7
Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin
{"title":"On the complex affine structures of SYZ-fibration of del Pezzo surfaces","authors":"Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin","doi":"10.4310/atmp.2022.v26.n6.a7","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n6.a7","url":null,"abstract":"Given any smooth cubic curve $E subseteq mathbb{P}^2$, we show that the complex affine structure of the special Lagrangian fibration of $mathbb{P}^2 : backslash : E$ constructed by Collins–Jacob–Lin [<b>12</b>] coincides with the affine structure used in Carl–Pomperla–Siebert [<b>15</b>] for constructing mirror. Moreover, we use the Floer-theoretical gluing method to construct a mirror using immersed Lagrangians, which is shown to agree with the mirror constructed by Carl–Pomperla–Siebert.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527187","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
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