Non-Abelian gauge theory for surface excitations of He3−B

Abstract

In He3−B, two atoms pair in an orbital angular momentum 1 spin triplet state above the phase transition temperature with SO(3)×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 get enhanced to SU(3)’s and the symmetry breaking is that of G=SU(3)×SU(3)×U(1) to H=SU(3). The theory of the resultant Goldstone 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 out. 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 flavor SU(3), and the Goldstone modes are the pions. Published by the American Physical Society 2024