Localization and holography in N=2 gauge theories

We compare exact results from Pestun's localization [1] of Su(N) N = 2* gauge theory on S-4 with available holographic models. While localization can explain the Coulomb branch vacuum of the holographic Pilch-Warner flow [2], it disagrees with the holographic Gauntlett et al. [3] vacuum of N = 2 super Yang-Mills theory. We further compute the free energy of the Pilch-Warner flow on S-4 and show that it disagrees with the localization result both for a finite S-4 radius, and in the S-4 decompactification limit. Thus, neither model represents holographic dual of supersymmetric S-4 localization of [1].