Ohnishi, Katsuhiko; Sakamoto, Makoto Novel phase structure of twisted \(\text{O}(N)\) \(\phi^ 4\) model on \(M^{D-1}\otimes S^ 1\). (English) Zbl 1050.81581 Phys. Lett., B 486, No. 1-2, 179-185 (2000). 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. Cited in 2 Documents MSC: 81T10 Model quantum field theories 81R40 Symmetry breaking in quantum theory PDFBibTeX XMLCite \textit{K. Ohnishi} and \textit{M. Sakamoto}, Phys. Lett., B 486, No. 1--2, 179--185 (2000; Zbl 1050.81581) Full Text: DOI arXiv References: [1] I. Antoniadis, S. Dimopoulos, G. Dvali, Nucl. Phys. B 516 (1998) 70, hep-ph/9710204; N. Arkani-Hamed, S. Dimopoulos, G. Dvali, Phys. Lett. B 429 (1998) 263, hep-ph/9803315; K.R. Dienes, E. Dudas, T. Gherghetta, Phys. Lett. B 436 (1998) 55, hep-ph/9803466; I. Antoniadis, S. Dimopoulos, A. Pomarol, M. Quiros, Nucl. Phys. B 544 (1999) 503, hep-ph/9810410; A. Delgado, A. Pomarol, M. Quiros, Phys. Rev. D 60 (1999) 095008, hep-ph/9812489.; I. Antoniadis, S. Dimopoulos, G. Dvali, Nucl. Phys. B 516 (1998) 70, hep-ph/9710204; N. Arkani-Hamed, S. Dimopoulos, G. Dvali, Phys. Lett. B 429 (1998) 263, hep-ph/9803315; K.R. Dienes, E. Dudas, T. Gherghetta, Phys. Lett. B 436 (1998) 55, hep-ph/9803466; I. Antoniadis, S. Dimopoulos, A. Pomarol, M. Quiros, Nucl. Phys. B 544 (1999) 503, hep-ph/9810410; A. Delgado, A. Pomarol, M. Quiros, Phys. Rev. D 60 (1999) 095008, hep-ph/9812489. [2] L. Randall.and R. Sundrum, Phy. Rev. Lett. 83 (1999) 3370, hep-ph/9905221; 83 (1999) 4690, hep-th/9906064; H. Hatanaka, M. Sakamoto, M. Tachibana, K. Takenaga, Prog. Theor. Phys. 102 (1999) 1213, hep-th/9909076.; L. Randall.and R. Sundrum, Phy. Rev. Lett. 83 (1999) 3370, hep-ph/9905221; 83 (1999) 4690, hep-th/9906064; H. Hatanaka, M. Sakamoto, M. Tachibana, K. Takenaga, Prog. Theor. Phys. 102 (1999) 1213, hep-th/9909076. [3] Dvali, G.; Shifman, M., Nucl. Phys. B, 504, 127 (1997), hep-th/9611213 [4] C.J. Isham, Proc. R. Soc. London A 362 (1978) 383; A 364 (1978) 591.; C.J. Isham, Proc. R. Soc. London A 362 (1978) 383; A 364 (1978) 591. [5] Y. Hosotani, Phys. Lett. B 126 (1983) 309; Ann. Phys. 190 (1989) 233.; Y. Hosotani, Phys. Lett. B 126 (1983) 309; Ann. Phys. 190 (1989) 233. [6] Sakamoto, M.; Tachibana, M.; Takenaga, K., Phy. Lett. B, 457, 33 (1999), hep-th/9902069 [7] M. Sakamoto. M. Tachibana, K. Takenaga, Phys. Lett. B 458 (1999) 231, hep-th/9902070; hep-th/9912229.; M. Sakamoto. M. Tachibana, K. Takenaga, Phys. Lett. B 458 (1999) 231, hep-th/9902070; hep-th/9912229. [8] B.F. Schutz, Geometrical methods of mathematical physics, Cambridge Univ. Press, Cambridge, 1980.; B.F. Schutz, Geometrical methods of mathematical physics, Cambridge Univ. Press, Cambridge, 1980. · Zbl 0462.58001 [9] L.H. Ford, T. Yoshimura, Phys. Lett. A 70 (1979) 89; D.J. Toms, Phys. Rev. D 21 (1980) 928; D 21 (1980) 2805.; L.H. Ford, T. Yoshimura, Phys. Lett. A 70 (1979) 89; D.J. Toms, Phys. Rev. D 21 (1980) 928; D 21 (1980) 2805. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.