Abstract
We construct the five-dimensional supergravity dual of the $\mathcal{N}=1^*$ mass deformation of the $\mathcal{N} =4$ supersymmetric Yang-Mills theory on $S^4$ and use it to calculate the universal contribution to the corresponding $S^4$ free energy at large 't Hooft coupling in the planar limit. The holographic RG flow solutions are smooth and preserve four supercharges. As a novel feature compared to the holographic duals of $\mathcal{N} = 1^*$ on $\mathbb{R}^4$, in our backgrounds the five-dimensional dilaton has a non-trivial profile, and the gaugino condensate is fixed in terms of the mass-deformation parameters. Important aspects of the analysis involve characterizing the ambiguities in the partition function of non-conformal $\mathcal{N}=1$ supersymmetric theories on $S^4$ as well as the action of S-duality on the $\mathcal{N}=1^*$ theory.
Highlights
The gauge/gravity duality [1,2,3] has provided many insights into the physics of stronglycoupled field theories
In generic N = 2 superconformal field theories (SCFTs) placed on S4 it was shown6 in [18, 19] that, in a regularization scheme preserving supersymmetry, the finite part of FS4 only has a shift ambiguity given by a sum of a holomorphic and an anti-holomorphic function of the exactly marginal couplings τi, N = 2 SCFT: FS4 → FS4 + f + f(τi)
9Our analysis generalizes to relevant deformations of other N = 1 SCFTs, but for concreteness we focus on the N = 1∗ case
Summary
The gauge/gravity duality [1,2,3] has provided many insights into the physics of stronglycoupled field theories. The holographic RG flows we present here for the duals of the one-mass and equal-mass N = 1∗ theories on S4 have not previously appeared in the literature For all these three models we can construct explicit supersymmetric solutions of the equations of motion of the maximal supergravity theory. This is a notable difference from the singular solutions constructed for the equal mass model in flat space in GPPZ [7] Such singular solutions are typical for holographic RG flows and present a challenge in understanding which supergravity singularities describe acceptable IR physics [48].
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