SU(2) gauge theory of gravity with topological invariants

TL;DR

This paper formulates a Hamiltonian approach to a generalized gravity theory in four dimensions that includes topological invariants, revealing a real SU(2) gauge structure with multiple coupling constants potentially significant in quantum gravity.

Contribution

It establishes a Hamiltonian formulation of a four-dimensional gravity theory with topological densities, showing its SU(2) gauge interpretation and the presence of multiple coupling constants.

Findings

The theory admits a real SU(2) gauge interpretation.

It contains three topological coupling constants.

The Hamiltonian formulation reveals seven first-class constraints.

Abstract

The most general gravity Lagrangian in four dimensions contains three topological densities, namely Nieh-Yan, Pontryagin and Euler, in addition to the Hilbert-Palatini term. We set up a Hamiltonian formulation based on this Lagrangian. The resulting canonical theory depends on three parameters which are coefficients of these terms and is shown to admit a real SU(2) gauge theoretic interpretation with a set of seven first-class constraints. Thus, in addition to the Newton's constant, the theory of gravity contains three (topological) coupling constants, which might have non-trivial imports in the quantum theory.