Perturbative Chern-Simons theory in the light-cone gauge. The one-loop vacuum polarization tensor in a gauge-invariant formalism

Abstract

Perturbative Chern-Simons (CS) theory, with gauge group SU( N), is studied in the physical light-cone gauge n σ A σ a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, we compute the vacuum polarization tensor to one-loop order. The regularized theory is consistent with BRS invariance. It is shown that the vacuum polarization tensor is UV finite and transverse, but contains one non-local term which is strictly gauge-dependent. A finite, non-multiplicative (gauge-dependent) wave function renormalization enables us to express the one-loop effective action as Γ one-loop( A μ (ren), k) = (( k + sign( k) c v)/4 π) S CS( A μ (ren), where S CS is the classical action and k is the bare Chern-Simons parameter.