Weyl-invariant higher curvature gravity theories

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2014
Dengiz, Suat
In this thesis, Weyl-invariant extensions of three-dimensional New Massive Gravity, generic n-dimensional Higher Curvature Gravity theories and three-dimensional Born-Infeld gravity theory are analyzed in details. As required by Weyl-invariance, the actions of these gauge theories do not contain any dimensionful parameter, hence the local symmetry is spontaneously broken in (Anti) de Sitter vacua in analogy with the Standard Model Higgs mechanism. In flat vacuum, symmetry breaking mechanism is more complicated: The dimensionful parameters come from dimensional transmutation in the quantum field theory; therefore, the conformal symmetry is radiatively broken (at two loop level in 3-dimensions and at one-loop level in 4-dimensions) a la Coleman-Weinberg mechanism. In the broken phases, save for New Massive Gravity, the theories generically propagate with a unitary (tachyon and ghost-free) massless tensor, massive (or massless) vector and massless scalar particles for the particular intervals of the dimensionless parameters. For New Massive Gravity, there is a massive Fierz-Pauli-type graviton. Finally, it is shown that n-dimensional Weyl-invariant Einstein-Gauss-Bonnet theory is the only unitary higher dimensional Weyl-invariant Quadratic Curvature Gravity theory.