(Non)-renormalization of the chiral vortical effect coefficient

We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D, dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula ∑ ∞ n=1 n = −1/12. We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large N limit.