Topological Quantum Gravity of the Ricci Flow

Understand

We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow on Riemannian manifolds.

• First we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric, with spatial diffeomorphism invariance and no gauge symmetry, associated with Hamilton's Ricci flow: Hamilton's flow equation appears as the localization equation of the primitive theory.
• Then we extend the primitive theory by gauging foliation-preserving spacetime symmetries.
• Crucially, all our theories are required to exhibit an ${\cal N}=2$ extended BRST symmetry.