Standard General Relativity from Chern-Simons Gravity

TL;DR

This paper demonstrates how standard five-dimensional General Relativity can emerge from Chern-Simons gravity models at a critical coupling point, using Lie algebra expansion techniques to connect the two theories.

Contribution

It introduces a mechanism where standard GR arises from Chern-Simons gravity in five dimensions via a specific algebraic expansion and critical point in coupling space.

Findings

Standard GR emerges at a critical point in five-dimensional Chern-Simons gravity.

Lie algebra S-expansion method constructs the necessary algebraic structures.

Results extend to arbitrary odd dimensions and suggest links to eleven-dimensional supergravity.

Abstract

Chern-Simons models for gravity are interesting because they provide with a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been the perceived remoteness from standard General Relativity, based on the presence of higher powers of the curvature in the Lagrangian (except, remarkably, for three-dimensional spacetime). Here we report on a simple model that suggests a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point in the space of couplings, where additional degrees of freedom and corresponding "anomalous" Gauss-Bonnet constraints drop out from the Chern-Simons action. To achieve this result, both the Lie algebra g and the symmetric g-invariant tensor that define the Chern-Simons Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite abelian semigroup S. The results are generalized to arbitrary odd dimensions, and the possible extension to the case of eleven-dimensional supergravity is briefly discussed.