Mass Deformed ABJM Theory on Three Sphere in Large N limit

In this paper the free energy of the mass deformed ABJM theory on S 3 in the large N limit is studied. We find a new solution of the large N saddle point equation which exists for an arbitrary value of the mass parameter, and compute the free energies for these solutions. We also show that the solution corresponding to an asymptotically AdS4 geometry is singular at a certain value of the mass parameter and does not exist over this critical value. It is not clear that what is the gravity dual of the mass deformed ABJM theory on S 3 for the mass parameter larger than the critical value.