Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual

We study phase structure of mass-deformed ABJM theory which is a three dimensional $mathcal{N}=6$ superconformal theory deformed by mass parameters and has the gauge group $text{U}(N)times text{U}(N)$ 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 $Nge k$, 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.