A homotopy BV algebra for Yang-Mills and color-kinematics

2019/12/06 by Michael Reiterer, Reiterer, Michael · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1912.03110

openalex publication_date 2019/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Minkowski wave operator. This homotopy structure implies BCJ/color-kinematics duality; a cobar construction yields a strict algebraic structure whose Feynman expansion for Yang-Mills tree amplitudes complies with the duality. It comes with a `syntactic kinematic algebra'.

Citations

• The Duality Between Color and Kinematics and its Applications

Cited by

• Operadic Calculus for Higher Colour-Kinematics Duality
• Superstring amplitudes from the field-theory limit: an n-point map at one loop
• The double copy as a doppelgänger
• Yang-Mills kinematic algebra via homotopy transfer from a worldline operator algebra
• The Double Copy of Maximal Supersymmetry in D=10

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