₂ Invariants of Hourglass Chains via Quadratic Denominator Reduction
We introduce families of four-regular graphs consisting of chains of hourglasses which are attached to a finite kernel. We prove a formula for the ₂ invariant of these hourglass chains, which only depends on the kernel. For different kernels, these hourglass chains typically give rise to different ₂...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| ISSN: | 1815-0659 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211427 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | ₂ Invariants of Hourglass Chains via Quadratic Denominator Reduction. Oliver Schnetz and Karen Yeats. SIGMA 17 (2021), 100, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We introduce families of four-regular graphs consisting of chains of hourglasses which are attached to a finite kernel. We prove a formula for the ₂ invariant of these hourglass chains, which only depends on the kernel. For different kernels, these hourglass chains typically give rise to different ₂ invariants. An exhaustive search for the ₂ invariants of hourglass chains with kernels that have a maximum of ten vertices provides Calabi-Yau manifolds with point-counts which match the Fourier coefficients of modular forms whose weights and levels are [4,8], [4,16], [6,4], and [9,4]. Assuming the completion conjecture, we show that no modular form of weight 2 and level ≤ 1000 corresponds to the ₂ of such hourglass chains. This provides further evidence in favour of the conjecture that curves are absent in ₂ invariants of ⁴ quantum field theory.
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| ISSN: | 1815-0659 |