Pub Date : 2022-01-01DOI: 10.4310/atmp.2022.v26.n7.a2
M. Dedushenko, Yifan Wang
{"title":"4d/2d → 3d/1d: A song of protected operator algebras","authors":"M. Dedushenko, Yifan Wang","doi":"10.4310/atmp.2022.v26.n7.a2","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n7.a2","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"51 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73536112","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 : 2022-01-01DOI: 10.4310/atmp.2022.v26.n7.a4
J. Hell, Phillipo Lappicy, C. Uggla
{"title":"Bifurcations and chaos in Hořava–Lifshitz cosmology","authors":"J. Hell, Phillipo Lappicy, C. Uggla","doi":"10.4310/atmp.2022.v26.n7.a4","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n7.a4","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"7 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73025206","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 : 2021-09-02DOI: 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.)
{"title":"Positive energy representations of affine algebras and Stokes matrices of the affine Toda equations","authors":"M. Guest, T. Otofuji","doi":"10.4310/atmp.2022.v26.n7.a3","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n7.a3","url":null,"abstract":"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.)","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"13 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74890045","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 : 2021-07-18DOI: 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.
{"title":"Probing the Big Bang with quantum fields","authors":"A. Ashtekar, T. Lorenzo, M. Schneider","doi":"10.4310/ATMP.2021.v25.n7.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n7.a1","url":null,"abstract":"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"7 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90291781","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 : 2021-06-11DOI: 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.
{"title":"Shifted symplectic reduction of derived critical loci","authors":"M. Anel, D. Calaque","doi":"10.4310/ATMP.2022.v26.n6.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n6.a1","url":null,"abstract":"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"25 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83320703","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 : 2021-05-25DOI: 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.
{"title":"General couplings of four dimensional Maxwell–Klein–Gordon system: Global existence","authors":"Mulyanto, F. Akbar, B. Gunara","doi":"10.4310/atmp.2022.v26.n1.a4","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n1.a4","url":null,"abstract":"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"285 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76135514","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 : 2021-05-12DOI: 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.
{"title":"Algebraic interplay between renormalization and monodromy","authors":"D. Kreimer, K. Yeats","doi":"10.4310/ATMP.2023.v27.n1.a4","DOIUrl":"https://doi.org/10.4310/ATMP.2023.v27.n1.a4","url":null,"abstract":"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"46 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86387285","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 : 2021-02-05DOI: 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.
{"title":"Supertranslation invariance of angular momentum","authors":"Po-Ning Chen, Mu-Tao Wang, Ye-Kai Wang, S. Yau","doi":"10.4310/atmp.2021.v25.n3.a4","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n3.a4","url":null,"abstract":"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"290 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77000284","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 : 2021-01-29DOI: 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:
{"title":"Almost contact structures on manifolds with a $G_2$ structure","authors":"Xenia de la Ossa, M. Larfors, Matthew Magill","doi":"10.4310/atmp.2022.v26.n1.a3","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n1.a3","url":null,"abstract":"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","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"187 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85452328","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 : 2021-01-18DOI: 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.
{"title":"The duality covariant geometry and DSZ quantization of abelian gauge theory","authors":"C. Lazaroiu, C. Shahbazi","doi":"10.4310/atmp.2022.v26.n7.a5","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n7.a5","url":null,"abstract":"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"17 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87283568","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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