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 that what is the gravity dual of the mass deformed ABJM theory on S 3 for the mass parameter larger than the critical value.

In this paper, using the localization technique we analyze the large N limit of the mass deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory on the three sphere with a finite mass parameter and finite Chern-Simons levels. We find two different solutions of the saddle point equations in the large N limit. With these solutions we compute the free energy and find that there is a first order phase transition. Our results may predict a phase transition in the dual gravity theory.Comment: 25 pages,3 figures; v2: typos corrected, a comment on solution II added, footnotes added, references adde

We study phase structure of mass-deformed ABJM theory which is a three dimensional N = 6 superconformal theory deformed by mass parameters and has the gauge group U(N ) × U(N ) with Chern-Simons levels (k, −k) which may have a gravity dual. We discuss that the mass deformed ABJM theory on S 3 breaks supersymmetry in a large-N limit if the mass is larger than a critical value. To see some evidence for this conjecture, we compute the partition function exactly, and numerically by using the Monte Carlo Simulation for small N . We discover that the partition function has zeroes as a function of the mass deformation parameters if N ≥ k, which supports the large-N supersymmetry breaking. We also find a solution to the large-N saddle point equations, where the free energy is consistent with the finite N result.

Three dimensional supersymmetric gauge theories are often in a gapped phase, in which SUSY is spontaneously broken, if all the matter fields are massive and decoupled in the low energy. We study this phase in the large N limit using the localization technique for the theory on the ellipsoid, which interpolates the round three sphere and the flat space compactified on S 1 . We find a large N saddle point solution for the gauge theory with some massive matter fields. This solution gives a vanishing (generalized) Polyakov loop in the flat space limit, thus, it corresponds to the confining phase at the leading order in the 1/N

We study the S 3 partition function of three-dimensional supersymmetric N = 4 U(N ) SQCD with massive matter multiplets in the infinite mass limit with the so-called Coulomb branch localization. We show that in the infinite mass limit a specific point of the Coulomb branch is selected and contributes dominantly to the partition function. Therefore, we can argue whether each multiplet included in the theory is effectively massless in this limit, even on S 3 , and conclude that the partition function becomes that of the effective theory on the specific point of the Coulomb branch in the infinite mass limit. In order to investigate which point of the Coulomb branch is dominant, we use the saddle point approximation in the large N limit because the solution of the saddle point equation can be regarded as a specific point of the Coulomb branch. Then, we calculate the partition functions for small rank N and confirm that their behaviors in the infinite mass limit are consistent with the conjecture from the results in the large N limit. Our result suggests that the partition function in the infinite mass limit corresponds to that of an interacting superconformal field theory.