Supersymmetry breaking in a large N gauge theory with gravity dual

Abstract

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.

Supersymmetry breaking phase in three dimensional large N gauge theories

“…It is expected that the Wilson loop does not include these zero modes and the contributions of the zero modes are canceled. 11 For k → 1, we find W ∼ N . Thus, for k = 1, the large N solution does not seem to correspond to the pure Chern-Simons theory.…”

“…In [12] and [10], we considered the large N limit of the round sphere partition function of the mass deformed ABJM theory and found that the large N solution of the saddle point equation, for which the free energy is proportional to N 3 2 , is valid only when ζ k < 1 4 , where ζ is the FI parameter and k is Chern-Simons level. If the mass is larger than this critical value, it was argued that the SUSY breaking occurs in [11]. In this phase, the large N solution of the confinement phase can be realized.…”

“…It may be interesting to study this phase through the exact results obtained by the localization technique because such a phase can appear in many interesting models. Indeed, such a spontaneously broken SUSY phase has been argued to appear in the large N mass deformed ABJM theory on S 3 , which will have a gravity dual with an asymptotic AdS 4 geometry, for an enough large mass parameter [10,11].…”

“…The theory which we will expect to have such a SUSY breaking phase is the mass deformed ABJM theory with a sufficiently large mass. In [12], [10] and [11], it has been argued that there is a critical mass in this theory and if the mass is larger than this critical value, the SUSY breaking occurs. In this phase, it is possible that the large N solution discussed in this paper is valid.…”

Aspects of massive gauge theories on three sphere in infinite mass limit

“…Then, we can approach the non-trivial dynamics triggered using these real mass parameter with the localization methods. In [4][5][6][7][8][9][10][11][12][13][14][15], the phase structure of mass-deformed gauge theories on S 3 is investigated.…”