Spin, torsion and violation of null energy condition in traversable wormholes

The static spherically symmetric traversable wormholes are analysed in the Einstein-Cartan theory of gravitation. In particular, we computed the torsion tensor for matter fields with different spin $S=0,1/2,1,3/2$. Interestingly, only for certain values of the spin, the torsion contribution to the Einstein-Cartan field equation allows one to satisfy both flaring-out condition and null energy condition. In this scenario, traversable wormholes can be produced by using usual (non-exotic) spinning matter.