Publications (7)0 Total impact
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ABSTRACT: We study supersymmetric and super Poincar\'e invariant deformations of
ten-dimensional super Yang-Mills theory and of its dimensional reductions. We
describe all infinitesimal super Poincar\'e invariant deformations of equations
of motion of ten-dimensional super Yang-Mills theory and its reduction to a
point; we discuss the extension of them to formal deformations. Our methods are
based on homological algebra, in particular, on the theory of L-infinity and
A-infinity algebras. The exposition of this theory as well as of some basic
facts about Lie algebra homology and Hochschild homology is given in
appendices.
10/2009;
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M. Movshev
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ABSTRACT: We make a preliminary algebraic study of supersymmetric deformations of N=1 Yang-Mills theory in dimension ten with an arbitrary gauge group. This is done in a context of Lie algebra deformation theory. The tangent space to the space of deformation is computed.
01/2006;
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M. Movshev
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ABSTRACT: This is a next paper from a sequel devoted to algebraic aspects of Yang-Mills theory. We undertake a study of deformation theory of Yang-Mills algebra YM - a ``universal solution'' of Yang-Mills equation. We compute (cyclic) (co)homology of YM.
10/2005;
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M. Movshev
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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 \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.
04/2005;
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M. Movshev
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ABSTRACT: We construct a supermanifold ST which turns to be an open subset of a superquadric Q(5|6) subset P^{3|3}times P^{3|3}. The Dolbeault algebra Omega^{0*}(ST) is quasiisomorphic to N=3, D=4 YM algebra in Batalin-Vilkovisky formulation. We construct a dbar-closed functional tr:Omega^{0*}(ST)=>C. We conjecture that Chern-Simons theory associated with a triple Omega^{0*}(ST)\otimes Mat_n,dbar,tr tr_{Mat_n}) is equivalent to N=3, D=4 YM theory with gauge group U_n in euclidean signature.
12/2004;
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ABSTRACT: In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with a paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally supersymmetric Yang-Mills theories. In this paper we collected those of our results which are correct without assumption of supersymmetry and used them to give rigorous proofs of some results of the cited paper. We consider two different algebraic interpretations of Yang-Mills theory - in terms of A_{\infty}-algebras and in terms of representations of Lie algebras (or associative algebras). We analyze the relations between these two approaches and calculate some Hochschild (co)homology of algebras in question.
05/2004;
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ABSTRACT: We consider ten-dimensional supersymmetric Yang–Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L∞- and A∞-algebras.We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer–Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern–Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra of (0,k)-forms on some supermanifold; the Lie algebra is tensor product of and matrix algebra. We construct several other algebras that are quasiisomorphic to and, therefore, also can be used to give BV formulation of 10D SUSY YM theory and its reductions. In particular, is quasiisomorphic to the algebra (B,d), constructed by Berkovits. The algebras and (B0,d) obtained from and (B,d) by means of reduction to a point can be used to give a BV-formulation of IKKT model. We introduce associative algebra SYM as algebra where relations are defined as equations of motion of IKKT model and show that Koszul dual to the algebra (B0,d) is quasiisomorphic to SYM.
Nuclear Physics B.
