Feynman symmetries of the Martin and $c_2$ invariants of regular graphs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909537875787776 |
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| author | Panzer, Erik Yeats, Karen |
| author_facet | Panzer, Erik Yeats, Karen |
| contents | For every regular graph, we define a sequence of integers, using the recursion of the Martin polynomial. This sequence counts spanning tree partitions and constitutes the diagonal coefficients of powers of the Kirchhoff polynomial. We prove that this sequence respects all known symmetries of Feynman period integrals in quantum field theory. We show that other quantities with this property, the $c_2$ invariant and the extended graph permanent, are essentially determined by our new sequence. This proves the completion conjecture for the $c_2$ invariant at all primes, and also that it is fixed under twists. We conjecture that our invariant is perfect: Two Feynman periods are equal, if and only if, their Martin sequences are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05299 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Feynman symmetries of the Martin and $c_2$ invariants of regular graphs Panzer, Erik Yeats, Karen Combinatorics High Energy Physics - Theory Mathematical Physics Algebraic Geometry 81Q30 (Primary) 05C70, 05C45 (Secondary) For every regular graph, we define a sequence of integers, using the recursion of the Martin polynomial. This sequence counts spanning tree partitions and constitutes the diagonal coefficients of powers of the Kirchhoff polynomial. We prove that this sequence respects all known symmetries of Feynman period integrals in quantum field theory. We show that other quantities with this property, the $c_2$ invariant and the extended graph permanent, are essentially determined by our new sequence. This proves the completion conjecture for the $c_2$ invariant at all primes, and also that it is fixed under twists. We conjecture that our invariant is perfect: Two Feynman periods are equal, if and only if, their Martin sequences are equal. |
| title | Feynman symmetries of the Martin and $c_2$ invariants of regular graphs |
| topic | Combinatorics High Energy Physics - Theory Mathematical Physics Algebraic Geometry 81Q30 (Primary) 05C70, 05C45 (Secondary) |
| url | https://arxiv.org/abs/2304.05299 |