A Non-Abelian Gauge Theory for Surface Excitations of $~^3$He-B
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911944995241984 |
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| author | Balachandran, A. P. |
| author_facet | Balachandran, A. P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Non-Abelian Gauge Theory for Surface Excitations of $~^3$He-B Balachandran, A. P. High Energy Physics - Theory Other Condensed Matter 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. |
| title | A Non-Abelian Gauge Theory for Surface Excitations of $~^3$He-B |
| topic | High Energy Physics - Theory Other Condensed Matter |
| url | https://arxiv.org/abs/2402.04714 |