### Holographic RG flows, on flat and curved manifolds and F-theorems

We carefully analyze the structure of holographic RG Flows dual to QFTs on Minkowski spacetime, and find several exotic possibilities beyond the known vanilla cases. We then proceed and study the holographic RG flows dual to QFTs on curved manifolds (spheres , de Sitter and AdS).

We analyze the general structure, and control fully the UV and IR asymptotic expansions. We also analyze the exotic flows found in flat space.

The de Sitter case provides an interesting interpretation of the on-shell action as a finite temperature free energy of the QFT.

We also study F-functions in the context of field theories on $S^3$, with the radius of $S^3$ playing the role of RG scale. We show that the on-shell action, evaluated over a set of holographic RG flow solutions, can be used to define good F-functions, which decrease monotonically along the RG flow from the UV to the IR for a wide range of examples. We check that these observations hold beyond holography for the case of a free fermion on $S^3$ ($\Delta=2$) and the free boson on $S^3$ ($\Delta=1$), resolving a long-standing problem regarding the non-monotonicity of the free energy for the free massive scalar. We also show that for a particular choice of entangling surface, we can define good F-functions from an entanglement entropy, which coincide with certain F-functions obtained from the on-shell action.

**Tuesday, 11th of June 2019, 14:30, sala Castagnoli**