Unified theory in the worldline approach

TL;DR

This paper applies the worldline approach to explore unified gauge theories like SU(5), SO(10), and others, revealing natural emergence of standard model representations and connections between different grand unified theories.

Contribution

It demonstrates the natural appearance of standard model representations within the worldline formalism for SU(5) and SO(10), and uncovers links between these theories and flipped SU(5), SU(6), and Pati-Salam models.

Findings

Standard model representations emerge naturally in SU(5) and SO(10) frameworks.

Connections between SU(5), flipped SU(5), and SO(10) are established.

The approach offers a unified perspective on various grand unified theories.

Abstract

We explore unified field theories based on the gauge groups $SU(5)$ and $SO(10)$ using the worldline approach for chiral fermions with a Wilson loop coupling to a background gauge field. Representing path ordering and chiral projection operators with functional integrals has previously reproduced the sum over the chiralities and representations of standard model particles in a compact way. This paper shows that for $SU(5)$ the $\bar{\mathbf{5}}$ and $\mathbf{10}$ representations -- into which the Georgi-Glashow model places the left-handed fermionic content of the standard model -- appear naturally and with the familiar chirality. We carry out the same analysis for flipped $SU(5)$ and uncover a link to $SO(10)$ unified theory. We pursue this by exploring the $SO(10)$ theory in the same framework, the less established unified theory based on $SU(6)$ and briefly consider the Pati-Salam model using $SU(4) \!\times \!SU(2)\! \times\! SU(2)$.