Holography for N = 1^∗ on S ⁴

We construct the five-dimensional supergravity dual of the N = 1^∗ mass deformation of the N = 4 supersymmetric Yang-Mills theory on S⁴ and use it to calculate the universal contribution to the corresponding S⁴ 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 N = 1^∗ on ℝ⁴, in our backgrounds the five-dimensional dilaton has a non-trivial profile, and the gaugino conden- sate 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 N = 1 supersymmetric theories on S⁴ as well as the action of S-duality on the N = 1^∗ theory.