Study Chern-Simons Theory Noncommutative Coupled Matter

Author(s)

Luiz Cleber Tavares de Brito

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2005-06-21

Examining board members

Marcelo Otavio Caminha Gomes; Antônio José Accioly; Carlos Eugenio Imbassahy Carneiro; Josif Frenkel; Adolfo Pedro Carvalho Malbouisson

• Advisor: Marcelo Otavio Caminha Gomes

Abstract

We consider 2+ 1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation minimally coupled to the Chern-Simons field is consistent in the sense that there are no nonintegrable infrared divergences. By contrast, dangerous infrared divergences occur if the fermion field belongs to the adjoint representation or if the coupling of scalar matter is considered instead. The superfield formulation of the supersymmetric Chern-Simons model is also analyzed and shown to be free of nonintegrable infrared singularities and actually finite if the matter field belongs to the fundamental representation of the supergauge group. In the case of the adjoint representation this only happens in a particular gauge. By analyzing the odd parity part of the gauge field two and three point vertex functions, the one-loop radiative correction to the Chern-Simons coefficient is computed in noncommutative Chern-Simons-Higgs model at zero and at high temperature. At high temperature, we show that the static limit of this correction is proportional to T but the first noncommutative correction increases as T log T. Our results are analytic functions of the noncommutative parameter. (AU)