Quantum Modular Ẑᴳ-Invariants
We study the quantum modular properties of Ẑᴳ-invariants of closed three-manifolds. Higher depth quantum modular forms are expected to play a central role for general three-manifolds and gauge groups . In particular, we conjecture that for plumbed three-manifolds whose plumbing graphs have n junctio...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2024 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212105 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantum Modular Ẑᴳ-Invariants. Miranda C.N. Cheng, Ioana Coman, Davide Passaro and Gabriele Sgroi. SIGMA 20 (2024), 018, 52 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862558534786351104 |
|---|---|
| author | Cheng, Miranda C.N. Coman, Ioana Passaro, Davide Sgroi, Gabriele |
| author_facet | Cheng, Miranda C.N. Coman, Ioana Passaro, Davide Sgroi, Gabriele |
| citation_txt | Quantum Modular Ẑᴳ-Invariants. Miranda C.N. Cheng, Ioana Coman, Davide Passaro and Gabriele Sgroi. SIGMA 20 (2024), 018, 52 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the quantum modular properties of Ẑᴳ-invariants of closed three-manifolds. Higher depth quantum modular forms are expected to play a central role for general three-manifolds and gauge groups . In particular, we conjecture that for plumbed three-manifolds whose plumbing graphs have n junction nodes with definite signature and for rank r gauge group , that Ẑᴳ is related to a quantum modular form of depth nr. We prove this for = SU(3) and for an infinite class of three-manifolds (weakly negative Seifert with three exceptional fibers). We also investigate the relation between the quantum modularity of Ẑᴳ-invariants of the same three-manifold with different gauge group . We conjecture a recursive relation among the iterated Eichler integrals relevant for Ẑᴳ with = SU(2) and SU(3), for negative Seifert manifolds with three exceptional fibers. This is reminiscent of the recursive structure among mock modular forms playing the role of Vafa-Witten invariants for SU(). We prove the conjecture when the three-manifold is moreover an integral homological sphere.
|
| first_indexed | 2026-03-13T07:41:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212105 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T07:41:19Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cheng, Miranda C.N. Coman, Ioana Passaro, Davide Sgroi, Gabriele 2026-01-28T13:55:40Z 2024 Quantum Modular Ẑᴳ-Invariants. Miranda C.N. Cheng, Ioana Coman, Davide Passaro and Gabriele Sgroi. SIGMA 20 (2024), 018, 52 pages 1815-0659 2020 Mathematics Subject Classification: 57K31; 57K16; 11F37; 11F27 arXiv:2304.03934 https://nasplib.isofts.kiev.ua/handle/123456789/212105 https://doi.org/10.3842/SIGMA.2024.018 We study the quantum modular properties of Ẑᴳ-invariants of closed three-manifolds. Higher depth quantum modular forms are expected to play a central role for general three-manifolds and gauge groups . In particular, we conjecture that for plumbed three-manifolds whose plumbing graphs have n junction nodes with definite signature and for rank r gauge group , that Ẑᴳ is related to a quantum modular form of depth nr. We prove this for = SU(3) and for an infinite class of three-manifolds (weakly negative Seifert with three exceptional fibers). We also investigate the relation between the quantum modularity of Ẑᴳ-invariants of the same three-manifold with different gauge group . We conjecture a recursive relation among the iterated Eichler integrals relevant for Ẑᴳ with = SU(2) and SU(3), for negative Seifert manifolds with three exceptional fibers. This is reminiscent of the recursive structure among mock modular forms playing the role of Vafa-Witten invariants for SU(). We prove the conjecture when the three-manifold is moreover an integral homological sphere. We would like to thank Boudewijn Bosch, Francesca Ferrari, and Sergei Gukov for fruitful discussions. The authors would also like to thank the referees for their suggestions. The work of M.C. is supported by an ERC starting grant H2020 # 640159 and NWO Vidi grant (number 016. Vidi.189.182), and the Ministry of Science and Technology of Taiwan (110-2115-M-001018-MY3). The work of I.C. is partly supported by the ERC starting grant H2020 # 640159 and NWO Vidi grant (number 016. Vidi.189.182). The work of D.P. is supported by the NWO Vidi grant (number 016. Vidi.189.182). I.C. and D.P. would like to thank Academia Sinica for its hospitality during the final stage of the project. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Modular Ẑᴳ-Invariants Article published earlier |
| spellingShingle | Quantum Modular Ẑᴳ-Invariants Cheng, Miranda C.N. Coman, Ioana Passaro, Davide Sgroi, Gabriele |
| title | Quantum Modular Ẑᴳ-Invariants |
| title_full | Quantum Modular Ẑᴳ-Invariants |
| title_fullStr | Quantum Modular Ẑᴳ-Invariants |
| title_full_unstemmed | Quantum Modular Ẑᴳ-Invariants |
| title_short | Quantum Modular Ẑᴳ-Invariants |
| title_sort | quantum modular ẑᴳ-invariants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212105 |
| work_keys_str_mv | AT chengmirandacn quantummodularzginvariants AT comanioana quantummodularzginvariants AT passarodavide quantummodularzginvariants AT sgroigabriele quantummodularzginvariants |