Pub Date : 2020-04-20DOI: 10.4310/atmp.2021.v25.n6.a1
A. Dancer, A. Hanany, F. Kirwan
We discuss symplectic and hyperkahler implosion and present candidates for the symplectic duals of the universal hyperkahler implosion for various groups.
我们讨论了辛和超卡勒内爆，并提出了各种群的普遍超卡勒内爆辛对偶的候选者。
{"title":"Symplectic duality and implosions","authors":"A. Dancer, A. Hanany, F. Kirwan","doi":"10.4310/atmp.2021.v25.n6.a1","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n6.a1","url":null,"abstract":"We discuss symplectic and hyperkahler implosion and present candidates for the symplectic duals of the universal hyperkahler implosion for various groups.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77841444","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 : 2020-04-15DOI: 10.4310/ATMP.2022.v26.n10.a11
Vikas Yadav, A. Misra
Construction of a top-down holographic dual of thermal QCD-like theories (equivalence class of theories which are UV-conformal, IR-confining and have fundamental quarks) {it at intermediate 't Hooft coupling} and the $G$-structure (torsion classes) classification of the underlying geometries (in the Infra Red (IR)/non-conformal sector in particular) of the {it non-supersymmetric} string/${cal M}$-theory duals, have been missing in the literature. We take the first important steps in this direction by studying the ${cal M}$ theory dual of large-$N$ thermal QCD-like theories at intermediate gauge and 't Hooft couplings and obtaining the ${cal O}(l_p^6)$ corrections arising from the ${cal O}(R^4)$ terms to the"MQGP"background (${cal M}$-theory dual of large-$N$ thermal QCD-like theories at intermediate gauge/string coupling, but large 't Hooft coupling) of cite{MQGP}. The main Physics lesson learnt is that there is a competition between non-conformal IR enhancement and Planckian and large-$N$ suppression and going to orders beyond the ${cal O}(l_p^6)$ is necessitated if the IR enhancement wins out. The main lesson learnt in Math is in the context of the differential geometry ($G$-structure classification) of the internal manifolds relevant to the string/${cal M}$-theory duals of large-$N$ thermal QCD-like theories, wherein we obtain for the first time inclusive of the ${cal O}(R^4)$ corrections in the Infra-Red (IR), the $SU(3)$-structure torsion classes of the type IIA mirror of cite{metrics} (making contact en route with Siegel theta functions related to appropriate hyperelliptic curves, as well as the Kiepert's algorithm of solving quintics), and the $G_2/SU(4)/Spin(7)$-structure torsion classes of the seven- and eight-folds associated with its ${cal M}$ theory uplift.
{"title":"On $M$-theory dual of large-$N$ thermal QCD-like theories up to $mathcal{O}(R^4)$ and $G$-structure classification of underlying non-supersymmetric geometries","authors":"Vikas Yadav, A. Misra","doi":"10.4310/ATMP.2022.v26.n10.a11","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n10.a11","url":null,"abstract":"Construction of a top-down holographic dual of thermal QCD-like theories (equivalence class of theories which are UV-conformal, IR-confining and have fundamental quarks) {it at intermediate 't Hooft coupling} and the $G$-structure (torsion classes) classification of the underlying geometries (in the Infra Red (IR)/non-conformal sector in particular) of the {it non-supersymmetric} string/${cal M}$-theory duals, have been missing in the literature. We take the first important steps in this direction by studying the ${cal M}$ theory dual of large-$N$ thermal QCD-like theories at intermediate gauge and 't Hooft couplings and obtaining the ${cal O}(l_p^6)$ corrections arising from the ${cal O}(R^4)$ terms to the\"MQGP\"background (${cal M}$-theory dual of large-$N$ thermal QCD-like theories at intermediate gauge/string coupling, but large 't Hooft coupling) of cite{MQGP}. The main Physics lesson learnt is that there is a competition between non-conformal IR enhancement and Planckian and large-$N$ suppression and going to orders beyond the ${cal O}(l_p^6)$ is necessitated if the IR enhancement wins out. The main lesson learnt in Math is in the context of the differential geometry ($G$-structure classification) of the internal manifolds relevant to the string/${cal M}$-theory duals of large-$N$ thermal QCD-like theories, wherein we obtain for the first time inclusive of the ${cal O}(R^4)$ corrections in the Infra-Red (IR), the $SU(3)$-structure torsion classes of the type IIA mirror of cite{metrics} (making contact en route with Siegel theta functions related to appropriate hyperelliptic curves, as well as the Kiepert's algorithm of solving quintics), and the $G_2/SU(4)/Spin(7)$-structure torsion classes of the seven- and eight-folds associated with its ${cal M}$ theory uplift.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141211897","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 : 2020-04-08DOI: 10.4310/atmp.2022.v26.n10.a1
P. Alcantara, P. M. Rios
Quantum or classical mechanical systems symmetric under $SU(2)$ are called spin systems. A $SU(2)$-equivariant map from $(n+1)$-square matrices to functions on the $2$-sphere, satisfying some basic properties, is called a spin-$j$ symbol correspondence ($n=2jinmathbb N$). Given a spin-$j$ symbol correspondence, the matrix algebra induces a twisted $j$-algebra of symbols. In this paper, we establish a new, more intuitive criterion for when the Poisson algebra of smooth functions on the $2$-sphere emerges asymptotically ($ntoinfty$) from the sequence of twisted $j$-algebras of symbols. This new, more geometric criterion, which in many cases is equivalent to the numerical criterion obtained in [Rios&Straume], is now given in terms of a classical (asymptotic) localization of the symbols of projectors (quantum pure states). For some important kinds of symbol correspondence sequences, classical localization of all projector-symbols is equivalent to asymptotic emergence of the Poisson algebra. But in general, such a classical localization condition is stronger than Poisson emergence. We thus also consider some weaker notions of asymptotic localization of projector-symbols. Finally, we obtain some relations between asymptotic localization of a symbol correspondence sequence and its quantizations of the classical spin system.
{"title":"Asymptotic localization of symbol correspondences for spin systems and sequential quantizations of $S^2$","authors":"P. Alcantara, P. M. Rios","doi":"10.4310/atmp.2022.v26.n10.a1","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n10.a1","url":null,"abstract":"Quantum or classical mechanical systems symmetric under $SU(2)$ are called spin systems. A $SU(2)$-equivariant map from $(n+1)$-square matrices to functions on the $2$-sphere, satisfying some basic properties, is called a spin-$j$ symbol correspondence ($n=2jinmathbb N$). Given a spin-$j$ symbol correspondence, the matrix algebra induces a twisted $j$-algebra of symbols. In this paper, we establish a new, more intuitive criterion for when the Poisson algebra of smooth functions on the $2$-sphere emerges asymptotically ($ntoinfty$) from the sequence of twisted $j$-algebras of symbols. This new, more geometric criterion, which in many cases is equivalent to the numerical criterion obtained in [Rios&Straume], is now given in terms of a classical (asymptotic) localization of the symbols of projectors (quantum pure states). For some important kinds of symbol correspondence sequences, classical localization of all projector-symbols is equivalent to asymptotic emergence of the Poisson algebra. But in general, such a classical localization condition is stronger than Poisson emergence. We thus also consider some weaker notions of asymptotic localization of projector-symbols. Finally, we obtain some relations between asymptotic localization of a symbol correspondence sequence and its quantizations of the classical spin system.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141216029","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 : 2020-03-29DOI: 10.4310/ATMP.2022.v26.n9.a12
A. Sakhnovich
We present a non-isospectral GBDT version of Backlund-Darboux transformation for the gravitational and $sigma$-model equations. New families of explicit solutions correspond to the case of GBDT with non-diagonal generalized matrix eigenvalues. An interesting integrable Ernst-type system, the auxiliary linear systems of which are non-isospectral canonical systems, is studied as well.
{"title":"Einstein, $sigma$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation","authors":"A. Sakhnovich","doi":"10.4310/ATMP.2022.v26.n9.a12","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n9.a12","url":null,"abstract":"We present a non-isospectral GBDT version of Backlund-Darboux transformation for the gravitational and $sigma$-model equations. New families of explicit solutions correspond to the case of GBDT with non-diagonal generalized matrix eigenvalues. An interesting integrable Ernst-type system, the auxiliary linear systems of which are non-isospectral canonical systems, is studied as well.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141220215","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 : 2020-03-19DOI: 10.4310/ATMP.2022.v26.n5.a9
M. Rossi
The present paper is dedicated to illustrating an extension of polar duality between Fano toric varieties to a more general duality, called emph{framed} duality, so giving rise to a powerful method of producing mirror partners of hypersurfaces and complete intersections in toric varieties, of any Kodaira dimension. In particular, the class of projective hypersurfaces and their mirror partners are studied in detail. Moreover, many connections with known Landau-Ginzburg mirror models, Homological Mirror Symmetry and Intrinsic Mirror Symmetry, are discussed.
{"title":"An extension of polar duality of toric varieties and its consequences in Mirror Symmetry","authors":"M. Rossi","doi":"10.4310/ATMP.2022.v26.n5.a9","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n5.a9","url":null,"abstract":"The present paper is dedicated to illustrating an extension of polar duality between Fano toric varieties to a more general duality, called emph{framed} duality, so giving rise to a powerful method of producing mirror partners of hypersurfaces and complete intersections in toric varieties, of any Kodaira dimension. In particular, the class of projective hypersurfaces and their mirror partners are studied in detail. Moreover, many connections with known Landau-Ginzburg mirror models, Homological Mirror Symmetry and Intrinsic Mirror Symmetry, are discussed.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73833962","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 : 2020-03-07DOI: 10.4310/atmp.2023.v27.n1.a3
T. Banks, W. Fischler
We revisit the construction of models of quantum gravity in d dimensional Minkowski space in terms of random tensor models, and correct some mistakes in our previous treatment of the subject. We find a large class of models in which the large impact parameter scattering scales with energy and impact parameter like Newton`s law. The scattering amplitudes in these models describe scattering of jets of particles, and also include amplitudes for the production of highly meta-stable states with all the parametric properties of black holes. These models have emergent energy, momentum and angular conservation laws, despite being based on time dependent Hamiltonians. The scattering amplitudes in which no intermediate black holes are produced have a time-ordered Feynman diagram space-time structure: local interaction vertices connected by propagation of free particles (really Sterman-Weinberg jets of particles). However, there are also amplitudes where jets collide to form large meta-stable objects, with all the scaling properties of black holes: energy, entropy and temperature, as well as the characteristic time scale for the decay of perturbations. We generalize the conjecture of Sekino and Susskind, to claim that all of these models are fast scramblers. The rationale for this claim is that the interactions are invariant under fuzzy subgroups of the group of volume preserving diffeomorphisms, so that they are highly non-local on the holographic screen. We review how this formalism resolves the Firewall Paradox.
{"title":"Holographic space-time, Newton’s law, and the dynamics of horizons","authors":"T. Banks, W. Fischler","doi":"10.4310/atmp.2023.v27.n1.a3","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n1.a3","url":null,"abstract":"We revisit the construction of models of quantum gravity in d dimensional Minkowski space in terms of random tensor models, and correct some mistakes in our previous treatment of the subject. We find a large class of models in which the large impact parameter scattering scales with energy and impact parameter like Newton`s law. The scattering amplitudes in these models describe scattering of jets of particles, and also include amplitudes for the production of highly meta-stable states with all the parametric properties of black holes. These models have emergent energy, momentum and angular conservation laws, despite being based on time dependent Hamiltonians. The scattering amplitudes in which no intermediate black holes are produced have a time-ordered Feynman diagram space-time structure: local interaction vertices connected by propagation of free particles (really Sterman-Weinberg jets of particles). However, there are also amplitudes where jets collide to form large meta-stable objects, with all the scaling properties of black holes: energy, entropy and temperature, as well as the characteristic time scale for the decay of perturbations. We generalize the conjecture of Sekino and Susskind, to claim that all of these models are fast scramblers. The rationale for this claim is that the interactions are invariant under fuzzy subgroups of the group of volume preserving diffeomorphisms, so that they are highly non-local on the holographic screen. We review how this formalism resolves the Firewall Paradox.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74824865","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 : 2020-03-04DOI: 10.4310/ATMP.2022.v26.n5.a6
Y. Kimura
We discuss a method for classifying the singularity types of 1/2 Calabi-Yau 3-folds, a family of rational elliptic 3-folds introduced in a previous study in relation to various U(1) factors in 6D F-theory models. A projective dual pair of del Pezzo manifolds recently studied by Mukai is used to analyze the singularity types. In particular, we studied the maximal rank seven singularity types of 1/2 Calabi-Yau 3-folds. The structures of the singular fibers are analyzed using blow-ups. Double covers of the 1/2 Calabi-Yau 3-folds yield elliptic Calabi-Yau 3-folds and applications to six-dimensional $N = 1$ F-theory on the Calabi-Yau 3-folds are also discussed. The deduced singular fibers have applications in studying the gauge groups formed in 6D F-theory compactifications. The blow-up methods used to analyze the singular fibers and sections utilized in this research might have applications in studying the U(1) factors and hypermultiplets charged under U(1) in 6D F-theory.
{"title":"Extremal $1/2$ Calabi–Yau $3$-folds and six-dimensional F-theory applications","authors":"Y. Kimura","doi":"10.4310/ATMP.2022.v26.n5.a6","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n5.a6","url":null,"abstract":"We discuss a method for classifying the singularity types of 1/2 Calabi-Yau 3-folds, a family of rational elliptic 3-folds introduced in a previous study in relation to various U(1) factors in 6D F-theory models. A projective dual pair of del Pezzo manifolds recently studied by Mukai is used to analyze the singularity types. In particular, we studied the maximal rank seven singularity types of 1/2 Calabi-Yau 3-folds. The structures of the singular fibers are analyzed using blow-ups. Double covers of the 1/2 Calabi-Yau 3-folds yield elliptic Calabi-Yau 3-folds and applications to six-dimensional $N = 1$ F-theory on the Calabi-Yau 3-folds are also discussed. The deduced singular fibers have applications in studying the gauge groups formed in 6D F-theory compactifications. The blow-up methods used to analyze the singular fibers and sections utilized in this research might have applications in studying the U(1) factors and hypermultiplets charged under U(1) in 6D F-theory.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72382604","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 : 2020-01-29DOI: 10.4310/ATMP.2022.v26.n1.a1
Kwokwai Chan, N. Leung, Qin Li
For a K"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^infty(X)[[hbar]],star_{BT})$ parametrized by points $z_0 in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}left( X,L^{otimes m}right) $ around $z_{0}$.
对于具有前量子线束$L$的Kähler流形$X$，我们给出了由点$z_0 in X$参数化的Berezin-Toeplitz变形量化代数$(C^infty(X)[[hbar]],star_{BT})$的一族表示的几何构造。关键思想是使用峰值截面来适当地定位$z_{0}$周围的希尔伯特空间$H^{0}left( X,L^{otimes m}right) $。
{"title":"A geometric construction of representations of the Berezin–Toeplitz quantization","authors":"Kwokwai Chan, N. Leung, Qin Li","doi":"10.4310/ATMP.2022.v26.n1.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n1.a1","url":null,"abstract":"For a K\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^infty(X)[[hbar]],star_{BT})$ parametrized by points $z_0 in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}left( X,L^{otimes m}right) $ around $z_{0}$.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73312469","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 : 2020-01-23DOI: 10.4310/ATMP.2022.v26.n3.a4
Matthias Ludewig, Guo Chuan Thiang
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current channels, which follow and are localised at the possibly complicated boundary. This index obstruction is shown to be insensitive to deformations of the domain boundary, so the phenomenon is generic for magnetic Laplacians modelling quantum Hall systems and Chern topological insulators. A key construction is a quasi-equivariant version of Roe's algebra of locally compact finite propagation operators.
{"title":"Cobordism invariance of topological edge-following states","authors":"Matthias Ludewig, Guo Chuan Thiang","doi":"10.4310/ATMP.2022.v26.n3.a4","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n3.a4","url":null,"abstract":"We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current channels, which follow and are localised at the possibly complicated boundary. This index obstruction is shown to be insensitive to deformations of the domain boundary, so the phenomenon is generic for magnetic Laplacians modelling quantum Hall systems and Chern topological insulators. A key construction is a quasi-equivariant version of Roe's algebra of locally compact finite propagation operators.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81466835","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 : 2020-01-02DOI: 10.4310/ATMP.2021.v25.n5.a3
F. Han, V. Mathai
In this paper, we extend the T-duality Hori maps in [arXiv:hep-th/0306062], inducing isomorphisms of twisted cohomologies on T-dual circle bundles, to graded Hori maps and show that they induce isomorphisms of two-variable series of twisted cohomologies on the T-dual circle bundles, preserving Jacobi form properties. The composition of the graded Hori map with its dual equals the Euler operator. We also construct Witten gerbe modules arising from gerbe modules and show that their graded twisted Chern characters are Jacobi forms under an anomaly vanishing condition on gerbe modules, thereby giving interesting examples.
{"title":"$T$-duality, Jacobi forms and Witten–Gerbe modules","authors":"F. Han, V. Mathai","doi":"10.4310/ATMP.2021.v25.n5.a3","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n5.a3","url":null,"abstract":"In this paper, we extend the T-duality Hori maps in [arXiv:hep-th/0306062], inducing isomorphisms of twisted cohomologies on T-dual circle bundles, to graded Hori maps and show that they induce isomorphisms of two-variable series of twisted cohomologies on the T-dual circle bundles, preserving Jacobi form properties. The composition of the graded Hori map with its dual equals the Euler operator. We also construct Witten gerbe modules arising from gerbe modules and show that their graded twisted Chern characters are Jacobi forms under an anomaly vanishing condition on gerbe modules, thereby giving interesting examples.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79483528","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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