2005/08/01 by Tewodros Amdeberhan, Arvind Ayyer, Amdeberhan, Tewodros +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th #math.CO
paper · pdf · doi:10.48550/arxiv.hep-th/0508014
31 pages, no figures, proof of the instanton equation included, more details on the higher dimensional case added
openalex publication_date 2005/08/01 · arxiv created 2006/01/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses (or vice versa). We find a large class of such operators and conjecture the moduli space to be the Hilbert Scheme of Points. Further, we apply this technique to find instanton solutions of a noncommutative N=1 supersymmetric gauge theory in six dimensions and show that this construction yields nontrivial solutions for other noncommutative gauge theories. The analysis is done in one complex dimension and the generalization of the result to higher dimensions is shown.