2005/03/22 by M. V. Movshev, M. Movshev, Movshev, M. · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Algebra (math.QA) #Quantum Chromodynamics and Particle Interactions #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/0503165
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openalex publication_date 2005/03/22 · arxiv created 2005/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we give a homological explanation of "pure spinors" in YM theories with minimal amount of supersymmetries. We construct A∞ algebras A for every dimension D=3,4,6,10, which for D=10 coincides with homogeneous coordinate ring of pure spinors with coordinate lambdaalpha. These algebras are Bar-dual to Lie algebras generated by supersymmetries, written in components. The algebras have a finite number of higher multiplications. The main result of the present note is that in dimension D=3,6,10 the algebra A⊗ Λ[θα]⊗ Matn with a differential D is equivalent to Batalin-Vilkovisky algebra of minimally supersymmetric YM theory in dimension D reduced to a point. This statement can be extended to nonreduced theories.