Related papers: Operadic Calculus for Higher Colour-Kinematics Dua…
This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we…
Yang-Mills gauge theory on Minkowski space supports a Batalin-Vilkovisky-infinity algebra structure, all whose operations are local. To make this work, the axioms for a BV-infinity algebra are deformed by a quadratic element, here the…
Color-kinematics duality states that the kinematic numerators of the cubic tree-level Yang-Mills scattering amplitudes obey the same symmetry properties that the color factors obey due to the Jacobi identity. We present a novel strategy for…
The transfer of the generating operations of an algebra to a homotopy equivalent chain complex produces higher operations. The first goal of this paper is to describe precisely the higher structure obtained when the unary operations commute…
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras on a fixed space M. his allows us to describe a notion of prefactorization algebra up to…
Colour-kinematics duality is a remarkable property of Yang-Mills theory. Its validity implies a relation between gauge theory and gravity scattering amplitudes, known as double copy. Albeit fully established at the tree level, its extension…
We prove a stronger version of the Kontsevich Formality Theorem for orientable manifolds, relating the Batalin-Vilkovisky (BV) algebra of multivector fields and the homotopy BV algebra of multidifferential operators of the manifold.
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus…
The purpose of this foundational paper is to introduce various notions and constructions in order to develop the homotopy theory for differential graded operads over any ring. The main new idea is to consider the action of the symmetric…
We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/$\Delta$ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other…
Field theories with kinematic Lie algebras, such as field theories featuring colour-kinematics duality, possess an underlying algebraic structure known as BV${}^{\color{gray} \blacksquare}$-algebra. If, additionally, matter fields are…
This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The…
We discuss the double copy formulation of Moyal-Weyl type noncommutative gauge theories from the homotopy algebraic perspective of factorisations of $L_\infty$-algebras. We define new noncommutative scalar field theories with rigid colour…
We show that if an operad is at the same time a cosimplicial object such that the respective structure maps are compatible with the operadic composition in a natural way, then one obtains a Gerstenhaber algebra structure on cohomology, and…
In the classical Batalin--Vilkovisky formalism, the BV operator $\Delta$ is a differential operator of order two with respect to the commutative product. In the differential graded setting, it is known that if the BV operator is…
The kinematic algebra of Yang-Mills theory can be understood in the framework of homotopy algebras: the $L_{\infty}$ algebra of Yang-Mills theory is the tensor product of the color Lie algebra and a kinematic space that carries a…
We introduce the notion of a BV-operator $\Delta=\{\Delta^n:V^n\longrightarrow V^{n-1}\}_{n\geq 0}$ on a homotopy $G$-algebra $V^\bullet$ such that the Gerstenhaber bracket on $H(V^\bullet)$ is determined by $\Delta$ in a manner similar to…
This is a survey on recent progress in algebraic deformation theory and the application of algebraic operads to its study. We review the classical homotopical tools in the theory of algebraic operads, namely Koszul duality. We give concrete…
This paper proves Koszul duality for coloured operads and uses it to introduce strongly homotopy operads as a suitable homotopy invariant version of operads. It shows that rational chains on configuration spaces of points in the plane form…
This paper is devoted to the calculation of Batalin-Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi-Yau generalized Weyl algebras. We firstly establish a Van den Bergh duality at the level of complex. Then based on…