an:06730224
Zbl 1364.81254
Edwards, James P.
Unified theory in the worldline approach
EN
Phys. Lett., B 750, 312-318 (2015).
00366741
2015
j
81V22 81R05 81T13
quantum electrodynamics; standard model; unification; Wilson loop
Summary: We explore unified field theories based on the gauge groups \(\mathrm{SU}(5)\) and \(\mathrm{SO}(10)\) 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 \(\mathrm{SU}(5)\) the \(\overline{5}\) 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 \(\mathrm{SU}(5)\) and uncover a link to \(\mathrm{SO}(10)\) unified theory. We pursue this by exploring the \(\mathrm{SO}(10)\) theory in the same framework, the less established unified theory based on \(\mathrm{SU}(6)\) and briefly consider the Pati-Salam model using \(\mathrm{SU}(4) \times \mathrm{SU}(2) \times \mathrm{SU}(2)\).