c(2) Invariants of Hourglass Chains via Quadratic Denominator Reduction

Schnetz O, Yeats K (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Symmetry Integrability and Geometry-Methods and Applications National Academy of Science of Ukraine

Book Volume: 17

DOI: 10.3842/SIGMA.2021.100

Abstract

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 phi(4) quantum field theory.

Authors with CRIS profile

Oliver Schnetz Lehrstuhl für Mathematik (Algebra und Geometrie)

Involved external institutions

University of Waterloo (UW) CA Canada (CA)

How to cite

APA:

Schnetz, O., & Yeats, K. (2021). c(2) Invariants of Hourglass Chains via Quadratic Denominator Reduction. Symmetry Integrability and Geometry-Methods and Applications, 17. https://dx.doi.org/10.3842/SIGMA.2021.100

MLA:

Schnetz, Oliver, and Karen Yeats. "c(2) Invariants of Hourglass Chains via Quadratic Denominator Reduction." Symmetry Integrability and Geometry-Methods and Applications 17 (2021).

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