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Novel phase structure of twisted \(\text{O}(N)\) \(\phi^ 4\) model on \(M^{D-1}\otimes S^ 1\). (English) Zbl 1050.81581
Summary: We study the \(O(N)\) \(\phi^4\) model compactified on \(M^{D-1}\otimes S^1\), which allows to impose twisted boundary conditions for the S\(^1\)-direction. The \(O(N)\) symmetry can be broken to H explicitly by the boundary conditions and further broken to I spontaneously by vacuum expectation values of the fields. The symmetries H and I are completely classified and the model turns out to have unexpectedly a rich phase structure. The unbroken symmetry I is shown to depend on not only the boundary conditions but also the radius of \(S^1\), and the symmetry breaking patterns are found to be unconventional. The spontaneous breakdown of the translational invariance is also discussed.

81T10 Model quantum field theories
81R40 Symmetry breaking in quantum theory
Full Text: DOI arXiv
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