The matreoshka of supersymmetric self-dual theories

TL;DR

This paper explores the hierarchical structure of supersymmetric self-dual theories, showing how solutions for higher N are built from N=0 solutions, simplifying the search for general solutions and revealing conserved current properties.

Contribution

It provides an explicit construction method for higher-N super self-dual solutions from N=0 solutions, highlighting the nested 'matreoshka' structure.

Findings

Higher-N solutions are built from N=0 solutions using a recursive construction.

Many conserved currents vanish in super self-dual systems.

The general local solutions for N>0 reduce to solutions of N=0 self-duality equations.

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.