Integer Quantization of the Chern-Simons Coefficient in a Broken Phase
  We consider a spontaneously broken nonabelian topologically massive gauge theory in a broken phase possessing a residual nonabelian symmetry. Recently there has been some question concerning the renormalization of the Chern-Simons coefficient in such a broken phase. We show that, in this broken vacuum, the renormalized ratio of the Chern-Simons coupling to the gauge coupling is shifted by $1/4\pi$ times an integer, preserving the usual integer quantization condition on the bare parameters. 
L. Chen, G. Dunne, K. Haller and E. Lim-Lombridas