Do Three Dimensions tell us Anything about a Theory of Everything?

TL;DR

This paper explores three-dimensional supersymmetric models as simplified analogs for understanding the potential of four-dimensional N=8 supergravity as a unified theory of everything, focusing on dynamical composite fields.

Contribution

It introduces extended supersymmetric three-dimensional coset models as toy laboratories to investigate dynamical aspects relevant to N=8 supergravity and the quest for a Theory of Everything.

Findings

Models can be extended to N=1 and N=2 supersymmetry.

Features of these models shed light on dynamical composite supermultiplets.

Open questions remain about their connection to N=8 supergravity.

Abstract

It has been conjectured that four-dimensional N=8 supergravity may provide a suitable framework for a `Theory of Everything', if its composite SU(8) gauge fields become dynamical. We point out that supersymmetric three-dimensional coset field theories motivated by lattice models provide toy laboratories for aspects of this conjecture. They feature dynamical composite supermultiplets made of constituent holons and spinons. We show how these models may be extended to include N=1 and N=2 supersymmetry, enabling dynamical conjectures to be verified more rigorously. We point out some special features of these three-dimensional models, and mention open questions about their relevance to the dynamics of N=8 supergravity.