First order discrete Faddeev gravity at the strongly varying fields

TL;DR

This paper explores a discrete, first-order formulation of Faddeev gravity with strongly varying tetrad fields, showing it reduces to a generalized Faddeev system that still recovers general relativity in the continuum limit.

Contribution

It introduces a discrete first-order Faddeev gravity model with strongly changing tetrad fields and demonstrates its reduction to a generalized Faddeev system consistent with GR.

Findings

Spectrum of elementary area is physically reasonable on classical backgrounds with large connections.

Discrete model with antiferromagnetic structure reduces to a generalized Faddeev system.

The continuum limit of the discrete model recovers the Einstein-Hilbert action of GR.

Abstract

We consider the Faddeev formulation of general relativity (GR), which can be characterized by a kind of $d$-dimensional tetrad (typically $d$=10) and a non-Riemannian connection. This theory is invariant w. r. t. the global, but not local, rotations in the $d$-dimensional space. There can be configurations with a smooth or flat metric, but with the tetrad that changes abruptly at small distances, a kind of "antiferromagnetic" structure. Previously, we discussed a first order representation for the Faddeev gravity, which uses the orthogonal connection in the $d$-dimensional space as an independent variable. Using the discrete form of this formulation, we considered the spectrum of (elementary) area. This spectrum turns out to be physically reasonable just on a classical background with large connection like rotations by $\pi$, that is, with such an "antiferromagnetic" structure. In the discrete first order Faddeev gravity, we consider such a structure with periodic cells and large connection and strongly changing tetrad field inside the cell. We show that this system in the continuum limit reduces to a generalization of the Faddeev system. The action is a sum of related actions of the Faddeev type and is still reduced to the GR action.