The large N limit of toric Chern-Simons matter theories and their duals

Abstract

We compute the large N limit of the localized three dimensional free energy of various field theories with known proposed AdS duals. We show that vector-like theories agree with the expected supergravity results, and with the conjectured F -theorem. We also check that the large N free energy is preserved by the three dimensional Seiberg duality for general classes of vector like theories. Then we analyze the behavior of the free energy of chiral-like theories by applying a new proposal. The proposal is based on the restoration of a discrete symmetry on the free energy before the extremization. We apply this procedure at strong coupling in some examples and we discuss the results. We conclude the paper by proposing an alternative geometrical expression for the free energy.

Sphere correlation functions and Verma modules

“…The N 3 2 behavior of the S 3 partition function was firstly discovered in [26] for ABJM model whose M-theory dual is AdS 4 × S 7 /Z k . It also shows up in a large class of 3d N = 3 [27][28][29][30] and N = 2 [31][32][33][34][35][36][37][38][39] Chern-Simons matter theories whose M-theory duals are AdS 4 × Y 7 where Y 7 are Sasaki-Einstein manifolds in such a way that the S 3 free energy is proportional to N with the coefficient depending on the volume of Y 7 . It would be interesting to give an holographic interpretation for our formula, perhaps by turning on the analogues of ζ and m on the supergravity side to study the dual to Z(m; ζ).…”

Wilson loops and the geometry of matrix models in AdS4/CFT3

“…Using equation (3.33), we know that for the toric case y · ζ M = 1 2 h M . If we introduce 36) we see that P rc is nothing but the intersection of P c with the characteristic hyperplane. But since the pre-image (under the moment map) of P c in Y 7 is the same as h −1 M (c), which changes topology every time we pass through a critical point of h M , we know that the topology of the pre-image of P rc in Y 7 also changes every time a critical point is crossed.…”

Is toric duality a Seiberg-like duality in (2 + 1)-d ?

“…(k, −k, k, −k) and also for Fano B 4 with Chern-Simons level (k, −2k, k) and the correct volumes of Q 2,2,2 /Z k and M 1,1,1 /Z k were reproduced [28,43]. Further for chiral theories, there is a discrepancy between the gauge theory superconformal index and the index on the corresponding gravity side at higher orders [46,47].…”

“…More details about the Seiberg-like duality in (2+1)-d can be found in [23][24][25][26][27][28][29]. The main theme of this paper is to check whether the (2+1)-d toric phases, with equal number of nodes in their quiver diagram, are always Seiberg-like duals (see flowchart in figure 2).…”