{"paper":{"title":"Phases with modular ground states for symmetry breaking by rank 3 and rank 2 antisymmetric tensor scalars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Stephen L. Adler","submitted_at":"2014-09-03T17:52:20Z","abstract_excerpt":"Working with explicit examples given by the 56 representation in $SU(8)$, and the 10 representation in $SU(5)$, we show that symmetry breaking of a group ${\\cal G}\\supset {\\cal G}_1 \\times {\\cal G}_2$ by a scalar in a rank three or two antisymmetric tensor representation leads to a number of distinct $modular$ ground states. For these broken symmetry phases, the ground state is periodic in an integer divisor $p$ of $N$, where $N>0$ is the absolute value of the nonzero $U(1)$ generator of the scalar component $\\Phi$ that is a singlet under the simple subgroups ${\\cal G}_1$ and ${\\cal G}_2$. Gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1180","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}