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First-order discrete Faddeev gravity at strongly varying fields. (English) Zbl 1378.83063

Summary: 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.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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