Noncommutative QCD, first-order-in-θ-deformed instantons and 't Hooft vertices

For commutative Euclidean time, we study the existence of fieldconfigurations that {\it a)} are formal power series expansions in$h\theta^{\m\n}$, {\it b)} go to ordinary (anti-)instantons as$h\theta^{\m\n}\to 0$, and {\it c)} render stationary the classical action ofEuclidean noncommutative SU(3) Yang-Mills theory. We show that thenoncommutative (anti-)self-duality equations have no solutions of this type atany order in $h\theta^{\m\n}$. However, we obtain all the deformations --calledfirst-order-in-$\theta$-deformed instantons-- of the ordinary instanton that,at first order in $h\theta^{\m\n}$, satisfy the equations of motion ofEuclidean noncommutative SU(3) Yang-Mills theory. We analyze the quantumeffects 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 $h\theta^{\m\n}$. Other issuesanalyzed in this paper are the existence at higher orders in $h\theta^{\m\n}$of topologically nontrivial solutions of the type mentioned above and theclassification of the classical vacua of noncommutative SU(N) Yang-Mills theorythat are power series in $h\theta^{\m\n}$.Comment: Latex. Some macros. No figures. 42 pages. Typos correcte