Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories

Understand

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.