Abstract
Shape dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable from classical general relativity. If taken seriously, it suggests that the space–time geometry picture that underlies general relativity can be replaced by a picture based on spatial conformal geometry. This classically well-understood trading of gauge symmetries opens new conceptual avenues in many approaches to quantum gravity. This paper focusses on the general implications for quantum gravity and effective field theory and considers the application of the shape dynamics picture in the exact renormalization group approaches to gravity, loop- and polymer-quantization approaches to gravity and low energy effective field theories. Also, the interpretation of known results is discussed through the shape dynamics picture, particularly holographic renormalization and the problem of time in canonical quantum gravity.
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