Geometric RG Flow

Understand

We define geometric RG flow equations that specify the scale dependence of the renormalized effective action Gamma[g] and the geometric entanglement entropy S[x] of a QFT, considered as functionals of the background metric g and the shape x of the entanglement surface.

• We show that for QFTs with AdS duals, the respective flow equations are described by Ricci flow and mean curvature flow.
• For holographic theories, the diffusion rate of the RG flow is much larger, by a factor R_{AdS}^2/\ell_s^2, than the RG resolution length scale.
• To derive our results.