𝑐₂ 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 𝑐₂ invariant of these hourglass chains, which only depends on the kernel. For different kernels, these hourglass chains typically give rise to different...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211427 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 𝑐₂ Invariants of Hourglass Chains via Quadratic Denominator Reduction. Oliver Schnetz and Karen Yeats. SIGMA 17 (2021), 100, 26 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 𝑐₂ invariant of these hourglass chains, which only depends on the kernel. For different kernels, these hourglass chains typically give rise to different 𝑐₂ invariants. An exhaustive search for the 𝑐₂ 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 𝑐₂ of such hourglass chains. This provides further evidence in favour of the conjecture that curves are absent in 𝑐₂ invariants of 𝜙⁴ quantum field theory.
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| ISSN: | 1815-0659 |