Unified theory in the worldline approach

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 $\bar{5}$ and $10$ 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 $SU(4)\times SU(2)\times SU(2)$.

10 Pages. Published version

References in corpus (3)

• Delta-function Interactions for the Bosonic and Spinning Strings and the Generation of Abelian Gauge Theory
• QED as the tensionless limit of the spinning string with contact interaction
• The Fermion Content of the Standard Model

Cited by in corpus (6)

• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• Contact interactions between particle worldlines
• Worldline colour fields and non-Abelian quantum field theory
• $U(N)$ Yang-Mills in non-commutative space time