The structure of all extended supersymmetric self-dual gauge theories

Abstract

Extended super self-dual systems have a structure reminiscent of a “matreoshka”: the N-extended theory has a structure largely determined by the ( N−1)-extended theory, and ultimately by the N = 0 core. Consequences of this phenomenon are explored. In particular, we present an explicit construction of local solutions of the higher- N super self-duality equations starting from any N = 0 self-dual solution. Our construction uses N = 0 solution data to produce N = 1 solution data, which in turn yields N = 2 solution data, and so on, each stage introducing a dependence of the solution on sufficiently many additional arbitrary functions to yield the most general supersymmetric solution having the initial N = 0 solution as the helicity +1 component. The problem of finding the general local solution of the N > 0 super self-duality equations therefore reduces to finding the general solution of the usual ( N = 0) self-duality equations. Another consequence of the matreoshka phenomenon is the vanishing of many observed currents, including the supercurrents, for super self-dual systems.