{"paper":{"title":"$N=1$ fermionic D3-branes in RNS formulation I. $C^\\infty$-Algebrogeometric foundations of $d=4$, $N=1$ supersymmetry, SUSY-rep compatible hybrid connections, and $\\widehat{D}$-chiral maps from a $d=4$ $N=1$ Azumaya/matrix superspace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.SG"],"primary_cat":"math.DG","authors_text":"Chien-Hao Liu, Shing-Tung Yau","submitted_at":"2018-08-15T09:28:44Z","abstract_excerpt":"As the necessary background to construct from the aspect of Grothendieck's Algebraic Geometry dynamical fermionic D3-branes along the line of Ramond-Neveu-Schwarz superstrings in string theory, three pieces of the building blocks are given in the current notes: (1) basic $C^\\infty$-algebrogeometric foundations of $d=4$, $N=1$ supersymmetry and $d=4$, $N=1$ superspace in physics, with emphasis on the partial $C^\\infty$-ring structure on the function ring of the superspace, (2) the notion of SUSY-rep compatible hybrid connections on bundles over the superspace to address connections on the Chan-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05011","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"}