new symmetries in Slavnov-extended noncommutative gauge theories

It is well known that the perturbative realization of noncommutative gauge field theories are plagued by a new phenomenon referred to as UV/IR mixing. A. A. Slavnov 1 has recently proposed an extension to such a model which might render them IR finite at higher loop order. In fact, this extension represents a topological term which, in certain gauges, introduces new symmetries to the model: In a recent peer reviewed publication [JHEP 0605:059, 2006], which was the result of an international cooperation with Prof. Francois Gieres of Université Claude Bernard (Lyon 1) and Prof. Olivier Piguet of Universidade Federal do Esprito Santo (UFES, Brazil), we have shown the appearance of a vector supersymmetry and an additional bosonic vectorial symmetry when using an axial gauge fixing. It is well known that symmetries, especially linear vector supersymmetries in topological field theories (à la Schwarz), lead to remarkable ultraviolet finiteness properties at the quantum level. Therefore, the presented research proposal is devoted to the following research aims: To continue the discussion of symmetries in Slavnov-extended gauge theories in axial as well as covariant gauge fixings and in 2-4 dimensional space-time. To discuss their consequences for quantum loop corrections and the appearance/absence of anomalies. We have shown2 that there exist certain two-loop graphs for which Slavnov`s trick does not get rid of the IR problems. However, there also exists a certain axial gauge 3 for which these contributions vanish. One can therefore assume, that in the sum of all two-loop graphs (1PI-corrections, full propagators, etc.) the problematic contributions will cancel also for a covariant gauge. This will be verified through explicit two- loop calculations. The Slavnov extension introduces new constraints to a gauge theory which will be analysed in the Dirac formalism4 . 1 Phys.Lett. B565:246, 2003; Teor.Mat.Fiz. 140N3:388, 2004. 2 JHEP 0511:041, 2005. 3 JHEP 0605:059, 2006. 4 P. A. M. Dirac, Lectures on quantum mechanics, New York, NY: Belfer Graduate School of Science (1964); M. Henneaux, C. Teitelboim, Quantization of gauge systems, Princeton University Press (1992).

It is well known that the perturbative realization of noncommutative gauge field theories are plagued by a new phenomenon referred to as UV/IR mixing. A. A. Slavnov 1 has recently proposed an extension to such a model which might render them IR finite at higher loop order. In fact, this extension represents a topological term which, in certain gauges, introduces new symmetries to the model: In a recent peer reviewed publication [JHEP 0605:059, 2006], which was the result of an international cooperation with Prof. Francois Gieres of Université Claude Bernard (Lyon 1) and Prof. Olivier Piguet of Universidade Federal do Esprito Santo (UFES, Brazil), we have shown the appearance of a vector supersymmetry and an additional bosonic vectorial symmetry when using an axial gauge fixing. It is well known that symmetries, especially linear vector supersymmetries in topological field theories (à la Schwarz), lead to remarkable ultraviolet finiteness properties at the quantum level. Therefore, the presented research proposal is devoted to the following research aims: To continue the discussion of symmetries in Slavnov-extended gauge theories in axial as well as covariant gauge fixings and in 2-4 dimensional space-time. To discuss their consequences for quantum loop corrections and the appearance/absence of anomalies. We have shown2 that there exist certain two-loop graphs for which Slavnov`s trick does not get rid of the IR problems. However, there also exists a certain axial gauge 3 for which these contributions vanish. One can therefore assume, that in the sum of all two-loop graphs (1PI-corrections, full propagators, etc.) the problematic contributions will cancel also for a covariant gauge. This will be verified through explicit two- loop calculations. The Slavnov extension introduces new constraints to a gauge theory which will be analysed in the Dirac formalism4 . 1 Phys.Lett. B565:246, 2003; Teor.Mat.Fiz. 140N3:388, 2004. 2 JHEP 0511:041, 2005. 3 JHEP 0605:059, 2006. 4 P. A. M. Dirac, Lectures on quantum mechanics, New York, NY: Belfer Graduate School of Science (1964); M. Henneaux, C. Teitelboim, Quantization of gauge systems, Princeton University Press (1992).