Standard model with gravity couplings

In this paper we examine the coupling of matter fields to gravity within the framework of the standard model of particle physics. The coupling is described in terms of Weyl fermions of a definite chirality, and employs only (anti-)self-dual or left-handed spin connection fields. We review the general framework for introducing the coupling using these fields, and show that conditions ensuring the cancellation of perturbative chiral gauge anomalies are not disturbed. We also explore a global anomaly associated with the theory, and argue that its removal requires that the number of fundamental fermions in the theory must be multiples of 16. In addition, we investigate the behavior of the theory under discrete transformations P, C, and T, and discuss possible violations of these discrete symmetries, including CPT, in the presence of instantons and the Adler-Bell-Jackiw anomaly.