Understand
A manifestly diffeomorphism invariant exact renormalization group requires extra diffeomorphism invariant ultraviolet regularisation at some effective cutoff scale $\Lambda$.
- This motivates construction of a `Parisi-Sourlas' supergravity, in analogy with the gauge theory case, where the superpartner fields have the wrong spin-statistics such that they can become Pauli-Villars regulator fields after spontaneous symmetry breaking.
- We show that in contrast to gauge theory, the free theory around flat space is already non-trivial and in a sense already displays some spontaneous symmetry breaking.
- We show that the fluctuating fields form multiplets whose mass matrices imply that the fields propagate into each other not only with the expected $1/p^2$ but also through propagators with improved ultraviolet properties, namely $1/p^4$ and $1/p^6$, despite the fact that the action contains a maximum of two space-time derivatives.