Split-complex representation of the universal hypermultiplet

TL;DR

This paper proposes that split-complex fields are a natural formulation for the scalar fields of the five-dimensional universal hypermultiplet, supported by solution analysis and their relation to Calabi-Yau moduli.

Contribution

It extends split-complex field representation from Euclidean to non-Euclidean cases and links it to the symplectic structure of hypermultiplets in Calabi-Yau compactifications.

Findings

Explicit instanton solutions for the hypermultiplet fields

Explicit 3-brane solutions coupled to the scalar fields

Evidence that split-complex formulation is favored in this context

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 non-trivial 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.