Weyl Symmetry in Stochastic Quantum Gravity

Understand

We propose that the gauge principle of d-dimensional Euclidean quantum gravity is Weyl invariance in its stochastic (d+1)-dimensional bulk.

• Observables are defined as depending only on conformal classes of d-dimensional metrics.
• We work with the second order stochastic quantization of Einstein equations in a (d+1)-dimensional bulk.
• There, the evolution is governed by the stochastic time, which foliates the bulk into Euclidean d-dimensional leaves.