2005/12/31 by C. P. Martin, Carmelo P Martín, Carlos Tamarit +1 · 9 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Commutative property #Euclidean geometry #Homotopy and Cohomology in Algebraic Topology #Instanton #Massless particle #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Order (exchange) #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/02/066
published in Journal of High Energy Physics 2006(02), 066 (Springer Nature) · Latex. Some macros. No figures. 42 pages. Typos corrected
arxiv created 2006/02/27 · openalex publication_date 2006/02/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
For commutative Euclidean time, we study the existence of field configurations that \it a) are formal power series expansions in hθ\m\n, \it b) go to ordinary (anti-)instantons as hθ\m\n→ 0, and \it c) render stationary the classical action of Euclidean noncommutative SU(3) Yang-Mills theory. We show that the noncommutative (anti-)self-duality equations have no solutions of this type at any order in hθ\m\n. However, we obtain all the deformations --called first-order-in-θ-deformed instantons-- of the ordinary instanton that, at first order in hθ\m\n, satisfy the equations of motion of Euclidean noncommutative SU(3) Yang-Mills theory. We analyze the quantum effects that these field configurations give rise to in noncommutative SU(3) with one, two and three nearly massless flavours and compute the corresponding 't Hooft vertices, also, at first order in hθ\m\n. Other issues analyzed in this paper are the existence at higher orders in hθ\m\n of topologically nontrivial solutions of the type mentioned above and the classification of the classical vacua of noncommutative SU(N) Yang-Mills theory that are power series in hθ\m\n.