Editing Chern–Simons theory (section)

===One-loop renormalization of the level===

If one adds matter to a Chern–Simons gauge theory then, in general it is no longer topological.  However, if one adds n [[Majorana fermion]]s then, due to the [[parity anomaly]], when integrated out they lead to a pure Chern–Simons theory with a one-loop [[renormalization]] of the Chern–Simons level by &minus;''n''/2, in other words the level k theory with n fermions is equivalent to the level ''k''&nbsp;&minus;&nbsp;''n''/2 theory without fermions.