Supersymmetric non-Abelian non-commutative Chern–Simons theory

Abstract

In this work, we study the three-dimensional non-Abelian noncommutative supersymmetric Chern-Simons model with the U (N ) gauge group. Using a superfield formulation, we prove that, for the pure gauge theory, the Green functions are one-loop finite in any gauge, if the gauge superpotential belongs to the fundamental representation of u(N ); this result also holds when matter in the fundamental representation is included. However, the cancellation of both ultraviolet and ultraviolet/infrared infrared divergences only happens in a special gauge if the coupling of the matter is in the adjoint representation. We also look into the finite one-loop quantum corrections to the effective action: in the pure gauge sector the Maxwell together with its corresponding gauge fixing action are generated; in the matter sector, the Chern-Simons term is generated, inducing a shift in the classical Chern-Simons coefficient. * Electronic address: alysson,mgomes,ajsilva@fma.if.usp.br † Electronic address: petrov@fisica.ufpb.br

Perturbative aspects of mass-deformed N=3 Chern-Simons-matter theory

“…The contributions to the two-point function of the gauge fields arising from the purely gauge/ghost sector can be found along the same lines as in [13], and within the one-loop order, even the overall coefficients will not be modified, thus, our results will be just the commutative limit of [13]. The corresponding Feynman diagrams are depicted at the Fig.…”

“…T C ). However, while in [13], it was necessary to consider separately planar and nonplanar parts, and namely the condition of vanishing the IR singularity arising from the non-planar part, implied in restrictions on the gauge group, in our case all contributions are proportional to the same integral 3 1 k 2 which identically vanishes within the dimensional regularization. Therefore, the UV divergent one-loop contribution to the two-point function of the gauge field arising from the purely gauge sector is identically zero.…”

“…The superficial degree of divergence of our theory is the same as for the usual supersymmetric Chern-Simons-matter theory [13]:…”

Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity

“….124) 10 Beyond the semi-classical level, the BV algebra faces potential perturbative anomalies due to infra-red-ultra-violet mixing [69], though the cancellation of topological anomalies of even and odd forms [70] are encouraging.…”

Equações de transporte na eletrodinâmica quântica não-comutativa

“…Uma boa discussão neste assunto foi feita por Szabo[37] e por Girotti[38]. Aplicações diversas de teorias não-comutativas foram feitas, citamos, por exemplo, estudos de teorias de Chern-Simons supersimétricas[42], modelos de Gross-Neveu tridimensional[43], estudos de renormalização da teoria[39,44], estudos de invariância de gauge quando θ depende das coordenadas[45], entre outros.…”