Localization and holography in N=2 gauge theories

TL;DR

This paper compares exact localization results of N=2^* gauge theories on S^4 with holographic models, revealing discrepancies that challenge the duality assumptions for these models.

Contribution

It provides a detailed comparison between localization results and holographic models, highlighting where they agree and where they diverge.

Findings

Localization explains the Coulomb branch vacuum of the Pilch-Warner flow.

Localization disagrees with the holographic vacuum of N=2 super Yang-Mills.

The free energy calculations do not match between localization and holography.

Abstract

We compare exact results from Pestun's localization 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, it disagrees with the holographic Gauntlett et.al 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 Pestun.