Solving mass-deformed holography perturbatively

Abstract

Abstract We study supergravity BPS equations which correspond to mass-deformation of some representative AdS/CFT examples. The field theory of interest are $$ \mathcal{N} $$ N = 4, D = 4 super Yang-Mills, the ABJM model in D = 3, and the Brandhuber-Oz fixed point in D = 5. For these gauge theories the free energy with mass terms for matter multiplets is calculable in large-N limit using supersymmetric localization technique. We suggest a perturbative method to solve the supergravity equations. For the dual of mass-deformed ABJM model we reproduce the known exact solutions. For the mass-deformed Brandhuber-Oz theory our method gives the holographic free energy in analytic form. For $$ \mathcal{N} $$ N = 2* theory our result is in good agreement with the localization result.