Parity and reality properties of the EPRL spinfoam

We study the parity behavior of the Lorentzian EPRL spinfoam model. We demonstrate that the vertex amplitude does not depend on the sign of the Immirzi parameter. We present numerical results for the transition amplitude and the graviton propagator in the large-spin 4-simplex approximation. The results suggest a simple relation between the contributions of the two parity-related critical points. Finally, we observe that the graviton propagator is not invariant under parity-odd permutations of equivalent nodes. Thus, the Lorentzian model has the same chirality problem as the Euclidean.