Supertwistors, Super Yang-Mills Theory and Integrability

Supertwistors are an important tool for understanding the properties of super Yang-Mills theory. I first give a brief introduction to supertwistor geometry and then explicitly discuss the Penrose-Ward (PW) transform, i.e., the relation between holomorphic vector bundles over supertwistor spaces and super gauge theories in four dimensions. Having presented the setup, I then use the PW transform for the construction of infinite dimensional hidden symmetry algebras in super gauge theories and exemplify the discussion by considering affine extensions of gauge and spacetime symmetries.