The Geometry of 6D, N = (1,0) Superspace and its Matter Couplings

TL;DR

This thesis explores the geometry of six-dimensional N=(1,0) superspace, solving Bianchi identities, analyzing superconformal structures, and studying matter couplings and the emergence of the Weyl multiplet.

Contribution

It provides a complete geometric analysis of 6D N=(1,0) superspace, including super-Weyl invariance and matter coupling constraints, advancing understanding of superconformal structures.

Findings

Solved Bianchi identities for 6D superspace torsion

Established super-Weyl invariance under scalar superfield transformations

Analyzed matter representations constrained by superconformal invariance

Abstract

This thesis is dedicated to the study of the geometry of six-dimensional superspace, endowed with the minimal amount of supersymmetry. In the first part of it, we unfold the main geometrical features of such superspace by solving completely the Bianchi identities for the constrained superspace torsion, which allow us to determine the full six-dimensional derivate superalgebra. Next, the conformal structure of the supergeometry is considered. Specifically, it is shown that the conventional torsion constraints remain invariant under super-Weyl transformations generated by a real scalar superfield parameter. In the second part of this work, the field content and superconformal matter couplings of the supergeometry are explored. The component field content of the Weyl multiplet is presented and the question of how this multiplet emerges in superspace is addressed. Finally, the constraints that conformal invariance imposes on some matter representations are analyzed.