de Sitter gauge theories and induced gravities

TL;DR

This paper explores how certain gauge theories in four-dimensional Euclidean space can lead to emergent gravity through dynamical mass generation and symmetry breaking, connecting gauge groups to spacetime geometries.

Contribution

It demonstrates that asymptotically free de Sitter and related gauge theories can induce effective geometries and gravity, revealing a mechanism for emergent spacetime structures.

Findings

Effective geometry can emerge from gauge theories with dynamical mass.

Symmetry breaking induces a transition from gauge groups to Lorentzian or Euclidean isometries.

The mass and running coupling influence the effective spacetime structure.

Abstract

Pure de Sitter, anti de Sitter, and orthogonal gauge theories in four-dimensional Euclidean spacetime are studied. It is shown that, if the theory is asymptotically free and a dynamical mass is generated, then an effective geometry may be induced and a gravity theory emerges. The asymptotic freedom and the running of the mass might account for an In\"on\"u-Wigner contraction which induces a breaking of the gauge group to the Lorentz group, while the mass itself is responsible for the coset sector of the gauge field to be identified with the effective vierbein. Furthermore, the resulting local isometries are Lorentzian for the anti de Sitter group and Euclidean for the de Sitter and orthogonal groups.