  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 AdS_4 geometry is singular at a certain
value of the mass parameter and does not exist over this critical value. It is
not clear what the gravity dual of the mass deformed ABJM theory on S^3 for the
mass parameter larger than the critical value is.
