  Shape Dynamics is a gauge theory based on spatial diffeomorphism- and
Weyl-invariance which is locally indistinguishable form classical General
Relativity. If taken seriously, it suggests that the spacetime--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.
I focus on the general implications for quantum gravity and effective field
theory and consider 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. I also discuss
the interpretation of known results through in the Shape Dynamics picture, in
particular holographic renormalization and the problem of time in canonical
quantum gravity.
