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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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