SU(INFINITY) (SUPER)GAUGE THEORIES AND SELF-DUAL (SUPER)GRAVITY

It is shown that SU(infinity) self-dual Yang-Mills equations on a four-dimensional flat Euclidean background are equivalent to Plebanski's second heavenly equation for the self-dual gravitational background, which is associated with the cotangent space of a suitable Riemann surface. The Riemann surface in question is nothing but the internal two-dimensional surface required in the formulation of SU(infinity) self-dual Yang-Mills theories. Such equivalence only occurs when a dimensional reduction has taken place. After a discussion of Euclidean Super-symmetries the results are generalized to ,elf-dual super-Yang-Mills theories and self-dual supergravity.