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Unified theory in the worldline approach. (English) Zbl 1364.81254
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 \(\mathrm{SU}(4) \times \mathrm{SU}(2) \times \mathrm{SU}(2)\).

MSC:
81V22 Unified quantum theories
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81T13 Yang-Mills and other gauge theories in quantum field theory
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