Naslov
Noncommutative gauge theories on R^3_λ : Perturbatively finite models

Autori
Gere, Antoine ; Jurić, Tajron ; Wallet, Jean-Christophe

Izvornik
The Journal of high energy physics (1126-6708) (2015), 12; 045-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Non-Commutative Geometry ; Differential and Algebraic Geometry ; Matrix Models ; Models of Quantum Gravity

Sažetak
We show that natural noncommutative gauge theory models on R3λ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of R3λ and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

POVEZANOST RADA