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Weyl-invariant extensions of three-dimensional New Massive Gravity, genericn-dimensional Quadratic Curvature Gravity theories and three-dimensionalBorn-Infeld gravity theory are analyzed in details. As required byWeyl-invariance, the actions of these gauge theories do not contain anydimensionful parameter; therefore the local symmetry is spontaneously broken in(Anti) de Sitter vacua in analogy with the Standard Model Higgs mechanism.About the flat vacuum, symmetry breaking mechanism is more complicated: Theconformal symmetry is radiatively broken (at two loop level in 3-dimensions andat one-loop level in 4-dimensions) a la Coleman-Weinberg mechanism and hencethe dimensionful parameters come from dimensional transmutation in the quantumfield theory. In the broken phases, save for New Massive Gravity, the theoriesgenerically propagate with a unitary (tachyon and ghost-free) massless tensor,massive (or massless) vector and massless scalar particles for the particularintervals of the dimensionless parameters. For New Massive Gravity, there is amassive Fierz-Pauli-type graviton. Finally, it is shown that n-dimensionalWeyl-invariant Einstein-Gauss-Bonnet theory is the only unitary higherdimensional Weyl-invariant Quadratic Curvature Gravity theory.

Weyl-invariant Higher Curvature Gravity Theories in n Dimensions and Mass Generation by Symmetry Breaking