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We have studied supersymmetric and super Poincaré invariant deformations of maximally supersymmetric gauge theories, in particular, of ten-dimensional super Yang-Mills theory and of its reduction to a point. We have described all infinitesimal super Poincaré invariant deformations of equations of motion and proved 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. In this paper we formulate some of the results we have obtained, but skip all proofs. However, we describe (in Sects. 2 and 3) the results of the theory of L-infinity and A-infinity algebras that serve as the main tool in our calculations.
KeywordsFormal Power Series Ghost Number Differential Algebra Hochschild Cohomology Cyclic Homology
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The work of both authors was partially supported by NSF grant No. DMS 0505735 and by grants DE-FG02-90ER40542 and PHY99-0794.
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