Yang-Mills theories in dimensions 3,4,6,10 and Bar-duality

Abstract

In this note we give a homological explanation of "pure spinors" in YM theories with minimal amount of supersymmetries. We construct A_{\infty} algebras A for every dimension D=3,4,6,10, which for D=10 coincides with homogeneous coordinate ring of pure spinors with coordinate lambda^{alpha}. 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\otimes Λ[θ^α]\otimes Mat_n 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.

arXiv commentSome references were added and few typos were corrected

References in corpus (1)

• On maximally supersymmetric Yang-Mills theories

Cited by in corpus (8)

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• Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
• Quantum Field Theory as Effective BV Theory from Chern-Simons
• Representation theory of super Yang-Mills algebras
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. I
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. II