Novel phase structure of twisted O(N) φ4 model on MD-1 ⊗ S1

We study the O(N) phi(4) model compactified on MD-1 circle times 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. (C) 2000 Elsevier Science B.V. All rights reserved.