Supersymmetry breaking in Chern-Simons-matter theories

Abstract

We investigate a relation between zeros of the partition function and supersymmetry breaking, conjectured by Morita and Niarchos, for a family of Chern-Simons-matter theories. We analyze the analytic structure of the free energy in the large N limit derived from the resolvent of the corresponding matrix model. We find that a branch point exists at the value of the 't Hooft coupling above which supersymmetry is known to be broken, confirming the conjecture.

Linear Chern-Simons-matter theories in the planar limit

“…which is the same as the expression obtained in [19]. The weak coupling limit corresponds to the limit ξ → −1.…”

“…where we have used Ω(η α ) = Ω α , which is shown in Appendix C. The residues Ω α are given as 19) and c α are given in terms of κ a by (3.3). Now, the 't Hooft couplings t a can be obtained very explicitly as…”

“…We have observed so far that the vevs of the Wilson loops vanish for values of t a corresponding to the supersymmetry breaking. For the theory under consideration, the condition for the supersymmetry breaking is N > k + m [19]. Then, one might expect that W above vanishes when t = 2πi + ν.…”

Supersymmetry breaking phase in three dimensional large N gauge theories

“…This may be the critical point which distinguishes the saddle point equation in the infinite mass limit with N f = 2 with other cases. 22 Let us consider the following point of Coulomb branches of the original SU(N) theory on the flat space:…”

“…Thus, for k = 1, the large N solution does not seem to correspond to the pure Chern-Simons theory. 12 In [21,22] the authors discuss this free energy of the pure Chern-Simons theory in the 't Hooft limit. They argue that when λ < 1 the integrand of the free energy has a logarithmic branch cut on a part of the integral interval and the integral is ill-defined.…”