Perturbative Chern-Simons theory on noncommutative Bbb R³

Abstract

Abstract. A U (N ) Chern-Simons theory on noncommutative R 3 is constructed as a θ-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that the theory is finite and θ µν -independent at the one loop level and that the calculations respect the restriction of the topological supersymmetry. Thus the topological θ-deformed Chern-Simons theory is an example of a model which is non-singular in the limit θ → 0.

A note on noncommutative Chern–Simons theories

“…We should recall that this limit is well-defined because (similar to the commutative case) we expect the quantum corrections on the Chern-Simons coupling 1 ν to appear only at one loop level, and the one loop result (2.3) remain to all higher order loops. However, starting from the pure Chern-Simons we still find the non-planar IR divergences [17]. The (2.3) is remarkable remembering the statistics of the noncommutative Chern-Simons particles (1.5) [21].…”

“…In this section we review the results of loop calculations for noncommutative Chern-Simons theories [17,18]. The action for the noncommutative extension of Chern-Simons theory is…”

“…The perturbative loop calculations have also been done for both pure NCCS [17] and for noncommutative Yang-Mills-Chern-Simons [18]. The pure Chern-Simons action at one loop level can once again be recovered by sending the gauge coupling to infinity.…”

“…we are not going to find any further IR divergence due to these terms. However, if we just start with the pure Chern-Simons we will persist with the IR divergences coming from non-planar diagrams [17]. This can be understood by noting that the Chern-Simons term introduces a topological mass term in the Yang-Mills action [5], and this mass term serves as a natural IR regulator, which, even in the pure Chern-Simons limit, tames the IR divergences of non-planar diagrams.…”

Supersymmetric non-Abelian non-commutative Chern–Simons theory

“…Matter can interact with the Chern-Simons superfield in two different ways. It can be in the fundamental representation, 1) or in the adjoint representation,…”