{"paper":{"title":"More on the admissible condition on differentiable maps $\\varphi: (X^{\\!A\\!z},E;\\nabla)\\rightarrow Y$ in the construction of the non-Abelian Dirac-Born-Infeld action $S_{DBI}(\\varphi,\\nabla)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.SG"],"primary_cat":"hep-th","authors_text":"Chien-Hao Liu, Shing-Tung Yau","submitted_at":"2016-11-29T00:10:36Z","abstract_excerpt":"In D(13.1) (arXiv:1606.08529 [hep-th]), we introduced an admissible condition on differentiable maps $\\varphi: (X^{\\!A\\!z}, E;\\nabla)\\rightarrow Y$ from an Azumaya/matrix manifold $X^{\\!A\\!z}$ (with the fundamental module $E$) with a connection $\\nabla$ on $E$ to a manifold $Y$ in order to resolve a pull-push issue in the construction of a non-Abelian-Dirac-Infeld action $S_{DBI}$ for $(\\varphi,\\nabla)$ and to render $\\nabla$ massless from the aspect of open strings. The admissible condition ibidem consists of two parts: Condition (1) and Condition (2). In this brief note, we examine these two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09439","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":""},"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"}