Operator Regularization and Large Noncommutative Chern Simons Theory

TL;DR

This paper investigates noncommutative Chern-Simons theory using operator regularization, analyzing one-loop effects and the transition to commutative models as noncommutativity vanishes.

Contribution

It introduces operator regularization methods to evaluate one-loop effects in noncommutative Chern-Simons theory and explores the smooth reduction to commutative models.

Findings

Both zeta- and eta-functions are necessary for one-loop calculations.

The noncommutative U(N) model reduces smoothly to the SU(N) commutative model as theta approaches zero.

The contributions from the two-point function are explicitly evaluated.

Abstract

We examine noncommutative Chern Simons theory using operator regularization. Both the zeta-function and the eta-function are needed to determine one loop effects. The contributions to these functions coming from the two point function is evaluated. The U(N) noncommutative model smoothly reduces to the SU(N) commutative model as the noncommutative parameter theta_{mu nu} vanishes.