Gravitational Goldstone fields from affine gauge theory

TL;DR

This paper explores a pure connection formalism for gravity using affine gauge theory, revealing that tetrads are nonlinear translational connections and that the metric's degrees of freedom are Goldstone bosons, which could simplify quantization.

Contribution

It introduces a nonlinear realization approach to affine gauge theories of gravity, clarifying the role of tetrads and the metric, and proposes a framework beneficial for quantization.

Findings

Tetrads are identified with nonlinear translational connections.

The metric degrees of freedom are Goldstone bosons, not independent potentials.

The approach may facilitate the quantization of gravity.

Abstract

In order to facilitate the application of standard renormalization techniques, gravitation should be decribed, if possible, in pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincare or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring the "hidden" piece responsible for this behavior within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide a general mathematical scheme clarifying the foundations of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the affine group, tetrads become identified with nonlinear translational connections; the anholonomic metric does not constitute any more an independent gravitational potential, since its degrees of freedom reveal to correspond to eliminable Goldstone bosons. This may be an important advantage for quantization.