We bring together different puzzles in physics beyond the Standard Model of particle physics. Within our model baryogenesis, neutrino mass, strong CP and dark matter puzzles are related. The common ingredient in connecting these puzzles is the Kalb-Ramond field, a two form present in the gravitational multiplet in the theory of closed strings. Leptons are fermions which we need to couple to gravitational degrees of freedom using a vierbein formalism. The presence of torsion provided by a Kalb-Ramond background leads us to firstly an effective model involving the Einstein-Cartan formulation of gravity, a gauge theory, in which coupling to fermions is via a covariant derivative and secondly to a mechanism for CPT violation. This picture emerges from a low energy string effective action obtained from a closed bosonic string theory after compactification to four dimensions. The Kalb-Ramond field in four dimensions can be identified with a pseudoscalar gravitational axion. Because of the presence of an axial anomaly this axion can couple with the gluon field, and in this way allows a connection with the strong CP problem and axionic dark matter.