Chern-Simons-like action induced radiatively in General Relativity
  The Chern-Simons-like gravitational action is evaluated explicitly in four dimensional space-time by radiative corrections at one-loop level. The calculation is performed in fermionic sector where the Dirac fermions interact with the background gravitational field, including the parity-violating term \bar\psi \bs\gamma_5\psi. The investigation takes into account the weak field approximation and dimensional regularization scheme. 
T. Mariz, J. R. Nascimento, E. Passos and R. F. Ribeiro