{"paper":{"title":"Spontaneously Broken Translational Invariance of Compactified Space","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"K.Takenaga (I.N.F.N, M. Sakamoto(Kobe Univ.), M. Tachibana(Kobe Univ.), Pisa)","submitted_at":"1999-02-10T11:09:35Z","abstract_excerpt":"We propose a mechanism to break the translational invariance of compactified space spontaneously. As a simple model, we study a real $\\phi^4$ model compactified on $M^{D-1}\\otimes S^1$ in detail, where we impose a nontrivial boundary condition on $\\phi$ for the $S^1$-direction. It is shown that the translational invariance for the $S^1$-direction is spontaneously broken when the radius $R$ of $S^1$ becomes larger than a critical radius $R^*$ and also that the model behaves like a $\\phi^4$ model on a single kink background for $R \\to \\infty$. It is pointed out that spontaneous breakdown of tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9902069","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9902069/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}