Noncommutative gauge theories on \( {\mathrm{\mathbb{R}}}_{\uplambda}^3 \) : perturbatively finite models

摘要: We show that natural noncommutative gauge theory models on $$ {\mathrm{\mathbb{R}}}_{\uplambda}^3 $$ can accommodate invariant harmonic terms, thanks to the existence of a relationship between center and components 1-form canonical connection. This latter object shows up naturally within present differential calculus. Restricting ourselves positive actions with covariant coordinates as field variables, suitable gauge-fixing leads family matrix quartic interactions kinetic operators compact resolvent. Their perturbative behavior is then studied. first compute 2-point 4-point functions at one-loop order subfamily these for which have symmetric form. find corresponding contributions are finite. extend this result arbitrary order. amplitudes ribbon diagrams finite all orders in perturbation. extends finally any whole obtained from above gauge-fixing. The origin discussed. Finally, particular model related integrable hierarchies indicated, partition function expressible product ratios determinants.