Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities
Abstract We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just N -sections, in order to study string dualities in four and fiv...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2019)170 |
| _version_ | 1818602536142110720 |
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| author | Cesar Fierro Cota Albrecht Klemm Thorsten Schimannek |
| author_facet | Cesar Fierro Cota Albrecht Klemm Thorsten Schimannek |
| author_sort | Cesar Fierro Cota |
| collection | DOAJ |
| description | Abstract We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just N -sections, in order to study string dualities in four and five dimensions as well as rigid limits in which gravity decouples. The generating functions are Jacobi-forms of Γ1(N) with the complexified fiber volume as modular parameter. The string coupling λ, or the ϵ± parameters in the rigid limit, as well as the masses of charged hypermultiplets and non-Abelian gauge bosons are elliptic parameters. To understand this structure, we show that specific auto-equivalences act on the category of topological B-branes on these geometries and generate an action of Γ1(N) on the stringy Kähler moduli space. We argue that these actions can always be expressed in terms of the generic Seidel-Thomas twist with respect to the 6-brane together with shifts of the B-field and are thus monodromies. This implies the elliptic transformation law that is satisfied by the generating functions. We use Higgs transitions in F-theory to extend the ansatz for the modular bootstrap to genus one fibrations with N -sections and boundary conditions fix the all genus generating functions for small base degrees completely. This allows us to study in depth a wide range of new, non-perturbative theories, which are Type II theory duals to the CHL ℤ N orbifolds of the heterotic string on K3 × T 2. In particular, we compare the BPS degeneracies in the large base limit to the perturbative heterotic one-loop amplitude with R + 2 F + 2 g − 2 $$ {R}_{+}^2{F}_{+}^{2g-2} $$ insertions for many new Type II geometries. In the rigid limit we can refine the ansatz and obtain the elliptic genus of superconformal theories in 5d. |
| first_indexed | 2024-12-16T13:08:50Z |
| format | Article |
| id | doaj.art-268f17ef76ec4a47a656363768c9eae0 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-16T13:08:50Z |
| publishDate | 2019-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-268f17ef76ec4a47a656363768c9eae02022-12-21T22:30:41ZengSpringerOpenJournal of High Energy Physics1029-84792019-11-0120191119610.1007/JHEP11(2019)170Topological strings on genus one fibered Calabi-Yau 3-folds and string dualitiesCesar Fierro Cota0Albrecht Klemm1Thorsten Schimannek2Bethe Center for Theoretical Physics, Universität BonnBethe Center for Theoretical Physics, Universität BonnFaculty of Physics, University of ViennaAbstract We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just N -sections, in order to study string dualities in four and five dimensions as well as rigid limits in which gravity decouples. The generating functions are Jacobi-forms of Γ1(N) with the complexified fiber volume as modular parameter. The string coupling λ, or the ϵ± parameters in the rigid limit, as well as the masses of charged hypermultiplets and non-Abelian gauge bosons are elliptic parameters. To understand this structure, we show that specific auto-equivalences act on the category of topological B-branes on these geometries and generate an action of Γ1(N) on the stringy Kähler moduli space. We argue that these actions can always be expressed in terms of the generic Seidel-Thomas twist with respect to the 6-brane together with shifts of the B-field and are thus monodromies. This implies the elliptic transformation law that is satisfied by the generating functions. We use Higgs transitions in F-theory to extend the ansatz for the modular bootstrap to genus one fibrations with N -sections and boundary conditions fix the all genus generating functions for small base degrees completely. This allows us to study in depth a wide range of new, non-perturbative theories, which are Type II theory duals to the CHL ℤ N orbifolds of the heterotic string on K3 × T 2. In particular, we compare the BPS degeneracies in the large base limit to the perturbative heterotic one-loop amplitude with R + 2 F + 2 g − 2 $$ {R}_{+}^2{F}_{+}^{2g-2} $$ insertions for many new Type II geometries. In the rigid limit we can refine the ansatz and obtain the elliptic genus of superconformal theories in 5d.https://doi.org/10.1007/JHEP11(2019)170D-branesF-TheoryString DualityTopological Strings |
| spellingShingle | Cesar Fierro Cota Albrecht Klemm Thorsten Schimannek Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities Journal of High Energy Physics D-branes F-Theory String Duality Topological Strings |
| title | Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities |
| title_full | Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities |
| title_fullStr | Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities |
| title_full_unstemmed | Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities |
| title_short | Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities |
| title_sort | topological strings on genus one fibered calabi yau 3 folds and string dualities |
| topic | D-branes F-Theory String Duality Topological Strings |
| url | https://doi.org/10.1007/JHEP11(2019)170 |
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