4d Lorentzian Holst action with topological terms

TL;DR

This paper explores the Hamiltonian formulation of a generalized first order action for general relativity, incorporating topological invariants, and analyzes the phase space structure and gauge transformations relevant for quantum gravity.

Contribution

It introduces a comprehensive Hamiltonian framework for the Holst action with additional topological terms, detailing their impact on the phase space and gauge structure in quantum gravity.

Findings

Inclusion of topological terms modifies the phase space structure.

Large SU(2) gauge transformations influence quantum gravity formulations.

The relationship between topological invariants and connection variables is clarified.

Abstract

We study the Hamiltonian formulation of the general first order action of general relativity compatible with local Lorentz invariance and background independence. The most general simplectic structure (compatible with diffeomorphism invariance and local Lorentz transformations) is obtained by adding to the Holst action the Pontriagin, Euler and Nieh-Yan invariants with independent coupling constants. We perform a detailed canonical analysis of this general formulation (in the time gauge) exploring the structure of the phase space in terms of connection variables. We explain the relationship of these topological terms, and the effect of large SU(2) gauge transformations in quantum theories of gravity defined in terms of the Ashtekar-Barbero connection.