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.Comment: Sections added. Text reviewed. References added. 14 pages, no
figures. Final version to appear in EPJ
