Flavored ABJM theory on the sphere and holographic F-functions

We study strongly coupled ABJM theory on the 3-sphere with massive quenched flavor using the AdS/CFT correspondence. The holographic dual consists of type IIA supergravity with probe D6-branes. The flavor mass is a relevant deformation driving an RG flow whose IR endpoint is pure ABJM theory. At non-zero mass, we find that the theory on the 3-sphere exhibits a quantum phase transition at a critical value of the sphere radius. The transition corresponds to a topology change in the D6-brane embeddings whose dual interpretation is the meson-melting transition. We perform the holographic computation of the free energy on 3-sphere and we use it to construct various candidate F-functions. These were recently proposed in the context of Einstein-scalar gravity to interpolate monotonically between the values of the sphere free energies of the UV and IR CFTs. We find that while the F-functions of the flavored ABJM theory have the correct UV and IR limits, they are not monotonic. We surmise that the non-monotonicity is related to the presence of the phase transition.