Split-complex representation of the universal hypermultiplet

Abstract

Split-complex fields usually appear in the context of Euclidean supersymmetry. In this paper, we propose that this can be generalized to the non-Euclidean case and that, in fact, the split-complex representation may be the most natural way to formulate the scalar fields of the five dimensional universal hypermultiplet. We supplement earlier evidence of this by studying a specific class of solutions and explicitly showing that it seems to favor this formulation. We also argue that this is directly related to the symplectic structure of the general hypermultiplet fields arising from nontrivial Calabi-Yau moduli. As part of the argument, we find new explicit instanton and 3-brane solutions coupled to the four scalar fields of the universal hypermultiplet.