Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories. I
Mikhail Movshev and A. Schwarz
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Submission date: 06. Oct. 2009
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We study supersymmetric and super Poincare invariant deformations of ten-dimensional super Yang-Mills theory and of its reduction to a point. We describe all infinitesimal super Poincare invariant deformations of equations of motion and prove that all of them are Lagrangian deformations and all of them can be extended 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.