Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Yang-Mills theories in dimensions 3,4,6,10 and Bar-duality   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 \Lambda[\theta^{\alpha}]\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.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat