On large N solution of Gaiotto-Tomasiello theory

Abstract

The planar solution is discussed for an N = 3 Chern-Simons-matter theory constructed recently by Gaiotto and Tomasiello. The planar resolvent is obtained in terms of contour integrals. If the sum of two Chern-Simons levels k 1 , k 2 is small, the expectation value of a supersymmetric Wilson loop grows exponentially with the total 't Hooft coupling, as is expected from AdS/CFT correspondence. If one of the Chern-Simons levels, say k 2 , is taken to infinity, for which one of the 't Hooft coupling constants becomes zero, then the exponential behavior disappears.

Notes on planar resolvents of Chern-Simons-matter matrix models

“…We focus our attention on a family of N ≥ 3 Chern-Simons-matter theories with the gauge group U(N 1 ) × U(N 2 ) coupled to an arbitrary number n of bi-fundamental hypermultiplets. The planar resolvents for such theories have been investigated in [5] [6] [22][23][24], however, explicit expressions for the resolvents have not been obtained so far except for ABJM theory and ABJ theory [25]. In this paper we show that, instead of the planar resolvent itself, its derivative can be determined explicitly for all theories mentioned above.…”

Supersymmetry breaking in Chern-Simons-matter theories

“…Here v 0 (z) is the same as the resolvent of pure Chern-Simons theory discussed above. v f (z) is obtained from (3.17) as [20] v…”

Toward the construction of the general multi-cut solutions in Chern-Simons matrix models

“…Before considering the multi-cut solutions, we first review the derivation of the DMP solution ( Figure 9 top-left) by using the technique in the previous section [51]. We assume the cut 16 Note that strong interactions work between µ i and ν j too in the saddle point equations (3.2), if they are separated by (2n + 1)πi.…”

“…For this reason, we do not consider the analytic solutions for these configurations in this article. We can perform this integral and obtain [51] w…”