The matreoshka of supersymmetric self-dual theories

Abstract

Extended super self-dual systems have a structure reminiscent of a ``matreoshka''. For instance, solutions for N=0 are embedded in solutions for N=1, which are in turn embedded in solutions for N=2, and so on. 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 conserved currents, including the supercurrents, for super self-dual systems.