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General Relativity can be reformulated as a diffeomorphism invariant gaugetheory of the Lorentz group, with Lagrangian of the type $f(F\wedge F)$, where$F$ is the curvature 2-form of the spin connection. A theory from this classwith a generic $f$ is known to propagate eight degrees of freedom: a masslessgraviton, a massive graviton and a scalar. General Relativity in this formalismavoids extra degrees of freedom because the function $f$ is special and leadsto the appearance of six extra primary constraints on the phase spacevariables. Our main new result is that there are other theories of the type$f(F\wedge F)$ that lead to six extra primary constraints. However, only in thecase of GR the dynamics is such that these six primary constraints getsupplemented by six secondary constraints, which gives the end result of twopropagating degrees of freedom. This is how uniqueness of GR manifests itselfin this ``pure spin connection" formalism. The other theories we discover areshown to give examples of irregular dynamical systems. At the linear levelaround (anti-)de Sitter space they have two degrees of freedom, as GeneralRelativity, with the extra ones manifesting themselves only non-linearly.

Pure Lorentz spin connection theories and uniqueness of General Relativity