Abstract:Some of the motivations and basic properties of noncommutative field models are presented. I also comment on recent developments in the understanding of these peculiar and intriguing theories.
“…The role of Poincaré supersymmetry for the cancellation of IR singularities has been extensively studied in the literature -see[14] for a review and further references 5. It has been shown[15] that Chern-Simons models without Poincaré supersymmetry may also be free of the IR singularities, depending on the gauge-fixing choice and on the coupling with matter.…”
We consider noncommutative U (1) gauge theory with the additional term, involving a scalar field λ, introduced by Slavnov in order to cure the infrared problem. We show that this theory, with an appropriate space-like axial gauge-fixing, exhibits a linear vector supersymmetry similar to the one present in the 2-dimensional BF model. This vector supersymmetry implies that all loop corrections are independent of the λAA-vertex and thereby explains why Slavnov found a finite model for the same gaugefixing.
“…The role of Poincaré supersymmetry for the cancellation of IR singularities has been extensively studied in the literature -see[14] for a review and further references 5. It has been shown[15] that Chern-Simons models without Poincaré supersymmetry may also be free of the IR singularities, depending on the gauge-fixing choice and on the coupling with matter.…”
We consider noncommutative U (1) gauge theory with the additional term, involving a scalar field λ, introduced by Slavnov in order to cure the infrared problem. We show that this theory, with an appropriate space-like axial gauge-fixing, exhibits a linear vector supersymmetry similar to the one present in the 2-dimensional BF model. This vector supersymmetry implies that all loop corrections are independent of the λAA-vertex and thereby explains why Slavnov found a finite model for the same gaugefixing.
“…Only special gauge theories are known to be free from these divergences (see e.g. the review [7]. Among them, let us mention Chern-Simons topological theory with particular couplings to matter [8], BF theories [9] and some supersymmetric Yang-Mills theories [10].…”
We show that the "topological BF-type" term introduced by Slavnov in order to cure the infrared divergences of gauge theories in noncommutative space can be characterized as the consequence of a new symmetry. This symmetry is a supersymmetry, generated by vector charges, of the same type as the one encountered in Chern-Simons or BF topological theories.
“…Já por volta da década de 1950 as interações fortes haviam sido bastante estudadas do ponto de vista fenomenológico. Uma interessante questão, do ponto de vista teórico, era a possibilidade de descrever todas interações em termos de teorias possuindo as mesmas características de simplicidade do Eletromagne- 1 O termo "gauge", que pode ser traduzido como calibre,teve sua origem na idéia desenvolvida por Weyl No próximo capítulo faremos uma breve introdução aos conceitos básicos de teoria de campos formulada em espaços não comutativos [9]. No capítulo 3 revisaremos…”
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