Operadic Calculus for Higher Colour-Kinematics Duality
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911319001661440 |
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| author | Medina-Mardones, Anibal M. Vallette, Bruno |
| author_facet | Medina-Mardones, Anibal M. Vallette, Bruno |
| contents | The search for algebraic foundations of colour-kinematics duality and the double-copy construction has brought into focus a generalization of Batalin--Vilkovisky algebras, referred to here as coexact BV-algebras and as $\textrm{BV}^\square$-algebras in other sources. While these structures capture the cubic sector, they fail to encode higher-valence phenomena, for which a homotopy-theoretic extension becomes necessary. This work introduces a conceptual notion of homotopy coexact BV-algebra, defined through the homotopical interplay of commutative and BV structures, and provides a concrete model in terms of generators and relations, obtained through an extension the theory of Koszul duality for operads. The resulting framework enables the systematic use of homotopical tools -- $\infty$-morphisms, homotopy transfer, rectification, and deformation theory -- and naturally accommodates the quartic-level structures recently identified in Yang--Mills theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operadic Calculus for Higher Colour-Kinematics Duality Medina-Mardones, Anibal M. Vallette, Bruno Mathematical Physics Algebraic Topology Quantum Algebra 18M70, 70S15, 18N40, 81T70 The search for algebraic foundations of colour-kinematics duality and the double-copy construction has brought into focus a generalization of Batalin--Vilkovisky algebras, referred to here as coexact BV-algebras and as $\textrm{BV}^\square$-algebras in other sources. While these structures capture the cubic sector, they fail to encode higher-valence phenomena, for which a homotopy-theoretic extension becomes necessary. This work introduces a conceptual notion of homotopy coexact BV-algebra, defined through the homotopical interplay of commutative and BV structures, and provides a concrete model in terms of generators and relations, obtained through an extension the theory of Koszul duality for operads. The resulting framework enables the systematic use of homotopical tools -- $\infty$-morphisms, homotopy transfer, rectification, and deformation theory -- and naturally accommodates the quartic-level structures recently identified in Yang--Mills theory. |
| title | Operadic Calculus for Higher Colour-Kinematics Duality |
| topic | Mathematical Physics Algebraic Topology Quantum Algebra 18M70, 70S15, 18N40, 81T70 |
| url | https://arxiv.org/abs/2512.12948 |