Abstract
Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a SO(4) - Yang-Mills theory. In addition to the gauge fields we include a vector field in the vector representation of the gauge group. The gauge - and diffeomorphism - invariant kinetic terms for these fields permit a well-defined euclidean functional integral, in contrast to metric gravity with the Einstein-Hilbert action. The propagators of all fields are well behaved at short distances, without tachyonic or ghost modes. The long distance behavior is governed by the composite metric and corresponds to general relativity. In particular, the graviton propagator is free of ghost or tachyonic poles despite the presence of higher order terms in a momentum expansion of the inverse propagator. This pregeometry seems to be a valid candidate for euclidean quantum gravity, without obstructions for analytic continuation to a Minkowski signature of the metric.
Highlights
Quantum field theories are defined by functional integrals
No well defined functional integral is known for a continuum formulation of quantum gravity based on the metric field
The fixed point involves many invariants, and it is not clear what approximation is needed in order to obtain a well defined propagator for the graviton without ghost or tachyonic instabilities [12]. This explains why so far no proposal for a simple classical action defining the functional integral for quantum gravity has been formulated in this approach
Summary
Quantum field theories are defined by functional integrals. For many models of particle physics one can employ an euclidean functional integral and continue analytically to Minkowski signature. Quantum gravity based on the metric may be a nonperturbatively renormalizable quantum field theory This is the case if the functional flow of a scale-dependent effective action [4] admits an ultraviolet fixed point. The fixed point involves many invariants, and it is not clear what approximation is needed in order to obtain a well defined propagator for the graviton without ghost or tachyonic instabilities [12] This explains why so far no proposal for a simple classical action defining the functional integral for quantum gravity has been formulated in this approach. The effective low energy theory is dominated by the terms with a small number of derivatives In leading order this turns out to be general relativity for the metric, with an Einstein-Hilbert action and a possible cosmological constant that we assume to be very small, as required by observation. IX discusses our findings and possible extensions in various directions
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