Refined BPS invariants of 6d SCFTs from anomalies and modularity
Abstract F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function Ztop of the refined topological string on these geometries captures the particle BPS spectrum of this clas...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP05(2017)130 |
| _version_ | 1819178844896100352 |
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| author | Jie Gu Min-xin Huang Amir-Kian Kashani-Poor Albrecht Klemm |
| author_facet | Jie Gu Min-xin Huang Amir-Kian Kashani-Poor Albrecht Klemm |
| author_sort | Jie Gu |
| collection | DOAJ |
| description | Abstract F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function Ztop of the refined topological string on these geometries captures the particle BPS spectrum of this class of theories compactified on a circle. Organizing Ztop in terms of contributions Z β at base degree β of the elliptic fibration, we find that these, up to a multiplier system, are meromorphic Jacobi forms of weight zero with modular parameter the Kähler class of the elliptic fiber and elliptic parameters the couplings and mass parameters. The indices with regard to the multiple elliptic parameters are fixed by the refined holomorphic anomaly equations, which we show to be completely determined from knowledge of the chiral anomaly of the corresponding SCFT. We express Z β as a quotient of weak Jacobi forms, with a universal denominator inspired by its pole structure as suggested by the form of Ztop in terms of 5d BPS numbers. The numerator is determined by modularity up to a finite number of coefficients, which we prove to be fixed uniquely by imposing vanishing conditions on 5d BPS numbers as boundary conditions. We demonstrate the feasibility of our approach with many examples, in particular solving the E-string and M-string theories including mass deformations, as well as theories constructed as chains of these. We make contact with previous work by showing that spurious singularities are cancelled when the partition function is written in the form advocated here. Finally, we use the BPS invariants of the E-string thus obtained to test a generalization of the Göttsche-Nakajima-Yoshioka K-theoretic blowup equation, as inspired by the Grassi-Hatsuda-Mariño conjecture, to generic local Calabi-Yau threefolds. |
| first_indexed | 2024-12-22T21:49:01Z |
| format | Article |
| id | doaj.art-54d2bbf54c8a41bbb517093ccd1d1879 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T21:49:01Z |
| publishDate | 2017-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-54d2bbf54c8a41bbb517093ccd1d18792022-12-21T18:11:25ZengSpringerOpenJournal of High Energy Physics1029-84792017-05-012017516310.1007/JHEP05(2017)130Refined BPS invariants of 6d SCFTs from anomalies and modularityJie Gu0Min-xin Huang1Amir-Kian Kashani-Poor2Albrecht Klemm3Laboratoire de Physique Théorique de l’ École Normale Supérieure, CNRS, PSL Research University, Sorbonne Universités, UPMCInterdisciplinary Center for Theoretical Study, University of Science and Technology of ChinaLaboratoire de Physique Théorique de l’ École Normale Supérieure, CNRS, PSL Research University, Sorbonne Universités, UPMCBethe Center for Theoretical Physics (BCTP), Physikalisches Institut, Universität BonnAbstract F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function Ztop of the refined topological string on these geometries captures the particle BPS spectrum of this class of theories compactified on a circle. Organizing Ztop in terms of contributions Z β at base degree β of the elliptic fibration, we find that these, up to a multiplier system, are meromorphic Jacobi forms of weight zero with modular parameter the Kähler class of the elliptic fiber and elliptic parameters the couplings and mass parameters. The indices with regard to the multiple elliptic parameters are fixed by the refined holomorphic anomaly equations, which we show to be completely determined from knowledge of the chiral anomaly of the corresponding SCFT. We express Z β as a quotient of weak Jacobi forms, with a universal denominator inspired by its pole structure as suggested by the form of Ztop in terms of 5d BPS numbers. The numerator is determined by modularity up to a finite number of coefficients, which we prove to be fixed uniquely by imposing vanishing conditions on 5d BPS numbers as boundary conditions. We demonstrate the feasibility of our approach with many examples, in particular solving the E-string and M-string theories including mass deformations, as well as theories constructed as chains of these. We make contact with previous work by showing that spurious singularities are cancelled when the partition function is written in the form advocated here. Finally, we use the BPS invariants of the E-string thus obtained to test a generalization of the Göttsche-Nakajima-Yoshioka K-theoretic blowup equation, as inspired by the Grassi-Hatsuda-Mariño conjecture, to generic local Calabi-Yau threefolds.http://link.springer.com/article/10.1007/JHEP05(2017)130Anomalies in Field and String TheoriesDifferential and Algebraic GeometryTopological Field TheoriesTopological Strings |
| spellingShingle | Jie Gu Min-xin Huang Amir-Kian Kashani-Poor Albrecht Klemm Refined BPS invariants of 6d SCFTs from anomalies and modularity Journal of High Energy Physics Anomalies in Field and String Theories Differential and Algebraic Geometry Topological Field Theories Topological Strings |
| title | Refined BPS invariants of 6d SCFTs from anomalies and modularity |
| title_full | Refined BPS invariants of 6d SCFTs from anomalies and modularity |
| title_fullStr | Refined BPS invariants of 6d SCFTs from anomalies and modularity |
| title_full_unstemmed | Refined BPS invariants of 6d SCFTs from anomalies and modularity |
| title_short | Refined BPS invariants of 6d SCFTs from anomalies and modularity |
| title_sort | refined bps invariants of 6d scfts from anomalies and modularity |
| topic | Anomalies in Field and String Theories Differential and Algebraic Geometry Topological Field Theories Topological Strings |
| url | http://link.springer.com/article/10.1007/JHEP05(2017)130 |
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