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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.

MSC:
81T10 Model quantum field theories
81R40 Symmetry breaking in quantum theory
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