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arXiv · 2402.04714

A Non-Abelian Gauge Theory for Surface Excitations of $~^3$He-B

A. P. Balachandran
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Abstract

In $~^3$He-B, two atoms pair in an orbital angular momentum $1$ spin triplet state above the phase transition temperature with $SO(3) \times SO(3)$ symmetry. Below the transition temperature, this symmetry is spontaneously broken to the diagonal $SO(3)$ due to spin-orbit coupling. Considerations based on effective potentials and solitons show that $SO(3)$'s gets enhanced to $SU(3)$'s and the symmetry breaking is that of $G= SU(3) \times SU(3)\times U(1)$ to $H= SU(3)$. The theory of the resultant Goldtsone modes can be naturally formulated as a gauge theory of $H$. Its Gauss law is treated here and shown to lead to surface states in a container with a dynamics governed by large gauge transformations. Observable consequences are pointed. The transference of the analysis to the chiral model of QCD is pointed out where $SU(3)$ are the left and right chiral groups, $U(1)$ is the axial $U(1)$ , the surviving symmetry is flavour $SU(3)$ and the Goldstone modes are the pions.

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A. P. Balachandran. 2024-02-07. A Non-Abelian Gauge Theory for Surface Excitations of $~^3$He-B. https://arxiv.org/abs/2402.04714

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