{"paper":{"title":"Analysis of $CP^{N-1}$ sigma models via projective structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. M. Grundland, S. Post","submitted_at":"2010-10-11T18:48:38Z","abstract_excerpt":"In this paper, we study rank-1 projector solutions to the completely integrable Euclidean $CP^{N-1}$ sigma model in two dimension and their associated surfaces immersed in the $su(N)$ Lie algebra. We reinterpret and generalize the proof of A.M. Din and W.J. Zakzrewski [1980] that any solution for the $CP^{N-1}$$ sigma model defined on the Riemann sphere with finite action can be written as a raising operator acting on a holomorphic one, or a lowering operator acting on a antiholomorphic one. Our proof is formulated in terms of rank-1 Hermitian projectors so it is explicitly gauge invariant and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2183","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"}