The Standard Model with gravity couplings

TL;DR

This paper explores how matter fields couple to gravity within the Standard Model framework, analyzing anomalies, symmetry violations, and conditions for a consistent theory with Weyl fermions and self-dual spin connections.

Contribution

It demonstrates that anomaly cancellation conditions are preserved and identifies the requirement that the number of fermions be multiples of 16 for global anomaly removal.

Findings

Chiral gauge anomalies remain canceled in the coupled theory.

Global anomaly considerations impose fermion number multiples of 16.

Possible violations of discrete symmetries like P, C, T, and CPT are discussed.

Abstract

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. It is known from the work of Ashtekar and others that such fields can furnish a complete description of gravity without matter. We 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.