Chern–Simons solutions of the chiral teleparallelism constraints of gravity

Abstract

Canonical transformations to complex variables in the teleparallelism equivalent (GR ∥) of general relativity are generated by the translational boundary term id C TT . In this Yang–Mills type approach, states constructed from the spatial translational Chern–Simons term C TT with self- or anti-self-dual torsion solve the Ashtekar type Hamiltonian constraints. The corresponding instantons are explicitly constructed and their implications for Wilson type Cartan circuits are outlined.