Operadic Calculus for Higher Colour-Kinematics Duality

Vortrag von Prof. Dr. Bruno Vallette

Datum: 20.10.25  Zeit: 14.45 - 15.45  Raum: ETH HG G 19.1

This talk aims at providing gauge field theory, in particular colour–kinematics duality and the double copy construction, with the required higher algebraic structures. From the algebro-homotopical perspective, a classical field theory is encoded by a cyclic homotopy Lie algebra whose Maurer–Cartan functional defines the action. For many gauge theories of interest, including Chern–Simons and Yang–Mills, this algebra splits as a tensor product of a cyclic Lie algebra, the colour Lie algebra, and a cyclic homotopy-commutative algebra, the kinematic algebra.

The duality between colour and kinematics, first observed by Bern–Carrasco–Johansson in the study of Yang–Mills amplitudes, suggests that the kinematic algebra carries a Lie-type structure. For theories with at most cubic interactions, this structure is captured by coexact Batalin-Vilkovisky (BV) algebras, algebraic objects dual to the exact BV algebras arising in Poisson geometry. To incorporate higher-order interactions, following ideas of M. Reiterer, a homotopy refinement of this notion becomes necessary.

The purpose of this talk is to provide a conceptual definition of homotopy coexact BV algebras, expressed in relation to homotopy commutative and BV algebras, together with a concrete operadic model. Our framework gives explicit presentations in terms of generating operations and relations and enables the systematic application of homotopical methods—including homotopy transfer, rectification, infinity-morphisms, and deformation theory—to the resulting algebras. The quartic-level structures recently identified in Yang–Mills theory fits naturally into this framework. 

This is a joint work with Anibal Medina-Mardones.