the fact that both chern–simons terms and majorana fermions are anomalous under deformations with odd instanton numbers is not a coincidence. when the pauli–villars mass for "n" majorana fermions is taken to infinity, redlich found that the remaining contribution to the partition function is equal to a chern–simons term at level −"n"/2. this means in particular that integrating out "n" charged majorana fermions renormalizes the chern–simons level of the corresponding gauge theory by −"n"/2. the fact that the chern–simons level is only allowed to take discrete values implies that the coupling constant can not enter into the correction to the level. this only occurs for the 1-loop correction, therefore the contribution of the majorana fermions to the chern–simons level may be precisely calculated at 1-loop and all higher loop corrections vanish.